Class Of Two-weight Linear Codes Research Articles

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.

Two classes of two-weight linear codes over finite fields

<abstract><p>Let $ p\equiv 1\pmod 4 $ be a prime, $ m $ a positive integer, $ \frac{\phi(p^m)}2 $ the multiplicative order of $ 2 $ modulo $ p^m $, and let $ q = 2^{ \frac{\phi(p^m)}2} $, where $ \phi(\cdot) $ is the Euler's function. In this paper, we construct two classes of linear codes over $ \Bbb F_q $ and investigate their weight distributions. By calculating two classes of special exponential sums, the desired results are obtained.</p></abstract>

Linear codes with few weights from cyclotomic classes and weakly regular bent functions

Linear codes with few weights constructed from defining sets have been extensively studied due to their applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Li et al. (Appl Algebra Eng Commun Comput 28(1):11–30, 2017) and Jian et al. (Finite Fields Appl 57:92–107, 2019), we propose a class of five-weight linear codes by choosing the defining set from cyclotomic classes, which includes a class of two-weight linear codes as a special case, and we also present two classes of two or three-weight linear codes by employing weakly regular bent functions. Besides, we obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound.

Complete weight enumerators of a class of two-weight linear codes

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. For an odd prime $p$ , we determine the complete weight enumerator and weight enumerator of a class of $p$ -ary linear codes by choosing a proper defining set. The results show that they have at most two weights and are suitable for applications in secret sharing schemes.

The weight distribution of a class of two-weight linear codes derived from Kloosterman sums

Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, a class of p-ary two-weight linear codes is constructed using a generic construction developed by Ding et al. recently, where p is a prime. Their length and weight distribution are closed-form expressions of Kloosterman sums over prime finite fields, and are completely determined when p = 2 and p = 3. The dual of this class of linear codes is also studied and is shown to be optimal or almost optimal in the binary case.

Secret Sharing Schemes from Linear Codes overFp + vFp

In principle, every linear code can be used to construct a secret sharing scheme. However, determining the access structure of the scheme is a very difficult problem. In this paper, we study MacDonald codes over the finite non-chain ring [Formula: see text], where p is a prime and [Formula: see text]. We provide a method to construct a class of two-weight linear codes over the ring. Then, we determine the access structure of secret sharing schemes based on these codes.

Two classes of two-weight linear codes

Two-weight linear codes have many wide applications in authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we present two classes of two-weight binary or ternary linear codes. In some cases, they are optimal or almost optimal. They can also be used to construct secret sharing schemes.