Application Of Secretion Research Articles

Several classes of new projective three-weight or four-weight linear codes and their applications in $ s $-sum sets

In this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes. Furthermore, basing on two classes of projective three-weight codes, we construct some $ s $-sum sets for any odd $ s>1 $.

Some codes over $${\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3} $$ and their applications in secret sharing schemes

Some codes over $${\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3} $$ and their applications in secret sharing schemes

Several classes of linear codes with few weights over finite fields

Linear codes with few weights have applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs. In this paper, we introduce a new flexible defining set, and consequently, we obtain several classes of t-weight linear codes over Fp, where t=4,5,6 and p is an odd prime. The parameters and weight distributions of the generated linear codes are fully determined using quadratic Gauss sums over finite fields. Moreover, two classes of optimal two-weight codes meeting the Griesmer bound are obtained from our constructions. Our results are heavily based on evaluating some exponential sums over finite fields. Computer experiments using MAGMA programs show that many (almost) optimal codes can be derived from our results.

Minimal linear codes from defining sets over [formula omitted

Minimal codes are a special type of linear codes, which have nice applications in secret sharing and secure two-party computation. How to construct new infinite family of minimal codes has been a hot topic in coding theory and cryptography. In this paper, by employing exponential sums, we study the Lee-weight distributions of several classes of linear codes from defining sets over the finite chain ring Fp+uFp and determine exactly the complete weight enumerator of their Gray images under the Gray map. Furthermore, we prove that the Gray images of these linear codes are new infinite families of minimal five-weight linear codes with wminwmax<p−1p.

Two new classes of projective two-weight linear codes

In this paper, for an odd prime p, several classes of two-weight linear codes over the finite field Fp are constructed from the defining sets, and then their complete weight enumerators are determined by employing character sums. These codes can be suitable for applications in secret sharing schemes. Furthermore, two new classes of projective two-weight codes are obtained, and then two new classes of strongly regular graphs are given.

Linear Codes from Two Weakly Regular Plateaued Balanced Functions

Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes. In this paper, we choose the defining sets from two distinct weakly regular plateaued balanced functions, based on a generic construction of linear codes. Then we construct a family of linear codes with at most five nonzero weights. Their minimality is also examined and the result shows that our codes are helpful in secret sharing schemes.

3-Aminopyridine Salicylidene: A Sensitive and Selective Chemosensor for the Detection of Cu(II), Al(III), and Fe(III) with Application to Real Samples.

Interest in developing selective and sensitive metal sensors for environmental, biological, and industrial applications is mounting. The goal of this work was to develop a sensitive and selective sensor for certain metal ions in solution. The goal was achieved via (i) preparing the sensor ((E)-2-((pyridine-3-ylimino)methyl)phenol) (3APS) using microwave radiation in a short time and high yield and (ii) performing spectrophotometric titrations for 3APS with several metal ions. 3APS, a Schiff base, was prepared in 5 min and in a high yield (95%) using microwave-assisted synthesis. The compound was characterized by FTIR, XRD, NMR, and elemental analysis. Spectrophotometric titration of 3APS was performed with Al(III), Ba(II), Cd(II), Co(II), Cu(II), Fe(III), Mn(II), Ni(II), and Zn(II). 3APS showed good abilities to detect Al(III) and Fe(III) ions fluorescently and Cu(II) ion colorimetrically. The L/M stoichiometric ratio was 2:1 for Cu(II) and 1:1 for Al(III) and Fe(III). Low detection limits (μg/L) of 324, 20, and 45 were achieved for Cu(II), Al(III), and Fe(III), respectively. The detection of aluminum was also demonstrated in antiperspirant deodorants, test strips, and applications in secret writing. 3APS showed high fluorescent selectivity for Al(III) and Fe(III) and colorimetric selectivity towards Cu(II) with detection limits lower than corresponding safe drinking water guidelines.

Two-weight or three-weight binary linear codes from cyclotomic mappings

Recently, linear codes with few weights have been studied extensively. These linear codes have wide applications in secret sharing schemes and authentication codes. In this paper, we introduce a new construction of defining sets using cyclotomic mappings and construct three new classes of binary linear codes with two or three weights. We also explicitly determine the weight distributions of these codes.

A conjugated photoresponsive dithienylethene–ferrocene system: applications in secret writing and decoding information

A ferrocene appended dithienylethene (DTE-Fc) bridged π-conjugated photochromic material that can be applicable in a lithographic technique (erasable ink) and deciphering secret codes.

Linear codes with few weights from weakly regular plateaued functions

Linear codes with few nonzero weights have wide applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Recently, Wu et al. (2020) obtained some few-weighted linear codes by employing bent functions. In this paper, inspired by Wu et al. and some pioneers' ideas, we use a kind of functions, namely, general weakly regular plateaued functions, to define the defining sets of linear codes. Then, by utilizing some cyclotomic techniques, we construct some linear codes with few weights and obtain their weight distributions. Notably, some of the obtained codes are almost optimal with respect to the Griesmer bound. Finally, we observe that our newly constructed codes are minimal for almost all cases.

A Construction of Minimal Linear Codes From Partial Difference Sets

In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical approach. We obtain new three-weight or four-weight minimal linear codes that do not satisfy the Ashikhmin-Barg condition by using partial difference sets. We show that our construction yields minimal linear codes that do not arise from cutting vectorial blocking sets, and also discuss their applications in secret sharing schemes.

Minimal Linear Codes From Characteristic Functions

Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb {F}_{q}$ to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536–6545, 2018]. By characteristic functions corresponding to some subspaces of $\mathbb {F}_{q}$ , we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536–6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067–7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.

Constructions of several classes of linear codes with a few weights

Recently, linear codes with a few weights have been constructed and extensively studied due to their applications in secret sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, we construct several classes of linear codes with a few weights over Fp, where p is an odd prime. The weight distributions of these constructed codes are also settled by applications of the theory of quadratic forms and Gauss sums over finite fields. Some of the linear codes obtained are optimal or almost optimal. The parameters of these linear codes are new in most cases. Moreover, two classes of MDS codes are obtained.

Minimal linear codes from Maiorana-McFarland functions

Minimal linear codes have important applications in secret sharing schemes and secure multi-party computation, etc. In this paper, we study the minimality of a kind of linear codes over GF(p) from Maiorana-McFarland functions. We first obtain a new sufficient condition for this kind of linear codes to be minimal without analyzing the weights of its codewords, which is a generalization of some works given by Ding et al. in 2015. Using this condition, it is easy to verify that such minimal linear codes satisfy wminwmax≤p−1p for any prime p, where wmin and wmax denote the minimum and maximum nonzero weights in a code, respectively. Then, by selecting the subsets of GF(p)s, we present two new infinite families of minimal linear codes with wminwmax≤p−1p for any prime p. In addition, the weight distributions of the presented linear codes are determined in terms of Krawtchouk polynomials or partial spreads.

Several Classes of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many construction methods for linear codes from functions have been proposed in the literature. In this paper, we generalize the recent construction methods given by Tang et al. in [IEEE Transactions on Information Theory, 62(3), 1166-1176, 2016] to weakly regular plateaued functions over finite fields of odd characteristic. We first construct three-weight linear codes from weakly regular plateaued functions based on the second generic construction and then determine their weight distributions. We also give a punctured version and subcode of each constructed code. We note that they may be (almost) optimal codes and can be directly employed to obtain (democratic) secret sharing schemes, which have diverse applications in the industry. We next observe that the constructed codes are minimal for almost all cases and finally describe the access structures of the secret sharing schemes based on their dual codes.

Complete weight enumerators of a class of linear codes over finite fields

<p style='text-indent:20px;'>We investigate a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. These codes have at most three weights and some of them are almost optimal so that they are suitable for applications in secret sharing schemes. This is a supplement of the results raised by Wang <i>et al.</i> (2017) and Kong <i>et al.</i> (2019).

Three Classes of Minimal Linear Codes Over the Finite Fields of Odd Characteristic

Minimal linear codes are a special subclass of linear codes and have significant applications in secret sharing and secure two-party computation. In this paper, we focus on constructing minimal linear codes with $\frac {w_{\min }}{w_{\max }}\leq \frac {p-1}{p}$ for any odd prime $p$ based on a generic construction of linear codes, where $w_{\min }$ and $w_{\max }$ denote the minimum and maximum nonzero weights in a code, respectively. First, we present two new infinite families of minimal linear codes with two or three weights by selecting suitable subcode of linear codes which are not minimal. Second, we also present an infinite family of minimal linear codes by employing partial spreads, which can be viewed as a generalization of the construction of Ding et al. In addition, we determine the weight distributions of all these minimal linear codes.

Complete weight enumerators of two classes of linear codes with a few weights

Linear codes with a few weights have important applications in secret sharing, authentication codes, data storage system, association schemes, and strongly regular graphs. Hence, the construction of linear codes with a few weights is an important research topic in coding theory. In this paper, we construct two new classes of linear codes with two and three weights, and determine their complete weight enumerators. Our work generalizes the results of Wang et al. (Discret Math 340(3):467–480, 2017).

Complete weight enumerators of a class of linear codes with two or three weights

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they have at most three weights and they are suitable for applications in secret sharing schemes. This is an extension of the results raised by Wang et al. (2017).

Two-Weight Linear Codes and Their Applications in Secret Sharing

Linear codes with few weighs have many applications in secret sharing. Determining the access structure of the secret sharing scheme based on a linear code is a very difficult problem. We provides a method to construct a class of two-weight torsion codes over finite non-chain ring. We determine the minimal codewords of these torsion codes over the finite non-chain ring. Based on the two-weight codes, we find the access structures of secret sharing schemes.