Cyclic Codes Research Articles (Page 1)

The study examines the influence of Asian sub-ethnic identity on the experiences of pre-medical students in the United States and Canada, aiming to understand how early interactions with the medical education system shape their pursuit of medicine. The researchers analyzed 132 discussion threads from popular online premedical school forums between June 2018 and 2023. The Asian Critical Theory framework guided the analysis along with cyclical inductive coding. Two major themes emerged: the homogenization of diverse Asian sub-ethnicities and external pressure related to sociocultural values. Terms like “over-represented minorities” contributed to the perception of Asians as a monolithic group, while expressions such as “Asian Parents” highlighted unique familial expectations. Non-Asian users often dismissed these barriers, reinforcing the model minority myth. The study emphasizes the negative consequences of framing Asians as a homogenous group in medical school admissions policies, perpetuating stereotypes, and overlooking the diversity within Asian sub-ethnic communities. The term “overrepresented” is critiqued for its role in homogenizing Asian identities and undermining the complexity of their experiences. These findings highlight the need for greater recognition of the nuanced challenges faced by Asian sub-ethnic medical trainees and the importance of dismantling stereotypes in medical education.

In this paper, we study [Formula: see text]-additive cyclic codes, where [Formula: see text] and [Formula: see text]. These codes are identified as [Formula: see text]-submodule of the ring [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are positive integers. We study the algebraic structure of these codes and set of generator polynomials for this codes. We show that the duals of [Formula: see text]-additive cyclic codes are also [Formula: see text]-additive cyclic codes. Moreover, we obtain minimal spanning sets of [Formula: see text]-cyclic codes, [Formula: see text]-cyclic codes and also [Formula: see text]-cyclic codes. Furthermore, we provide some examples for [Formula: see text]-cyclic codes and their generating sets.

Let p be a prime and Fp a finite field of order p. This paper investigates cyclic codes over the ring Rp2,u=Zp2+uZp2 of order p4, where the nilpotent element u satisfies u2=0 and pu≠0. The condition u2=0 with pu≠0 is crucial, as it creates a nontrivial interaction between the components of the ring, allowing the construction of new codes with enhanced structural and distance properties. We provide explicit generating sets for cyclic codes over Rp2,u and study fundamental parameters such as their rank and Hamming distance. In the case gcd(n,p)=1, we show that cyclic codes can be generated by just two polynomials, which allows a complete determination of their rank and minimal Hamming distance distributions. Furthermore, using the Gray map from Rp2,u to Fp4, we construct all but one of the ternary optimal codes of length 12 as images of cyclic codes over R32,u, with computations verified using the Magma system.

ABSTRACTEnsuring secure communication in the digital era is of paramount importance. This study introduces a novel encryption model that combines ‐cyclic codes with the one‐time pad (OTP) method over Eisenstein–Jacobi integers, achieving information‐theoretic security. The method constructs a finite ring over Eisenstein–Jacobi integers, generates one‐time keys from ‐cyclic codewords, and uses these keys to encrypt messages, guaranteeing each key is used only once. Multiple plausible ciphertexts are produced for each plaintext, making unauthorized decryption infeasible. Key findings show that the scheme provides high computational efficiency and robust resistance to cryptographic attacks, outperforming existing code‐based and public‐key systems. Security scales with prime selection, as longer codewords and keys increase protection. The algebraic structure of Eisenstein–Jacobi integers enables efficient key generation and encryption operations, making the model suitable for critical security applications. Existing OTP and cyclic code‐based encryption systems are typically limited to binary fields or specific rings, constraining key diversity and scalability. By extending OTP to ‐cyclic codes over Eisenstein–Jacobi integers, the proposed model overcomes these limitations, providing a larger key space and more complex encryption structure. Code‐based encryption, including cyclic codes, offers quantum‐resistant security. This feature aligns the proposed OTP model with post‐quantum cryptography (PQC). This work demonstrates that combining cyclic codes with OTP creates an unbreakable and practical encryption framework, providing resistance against both conventional and quantum attacks.

In this paper, the structures of linear codes over the quaternion rings with coe cient from Zp, Hp = Zp+Zpi+Zpj+Zpk are given, where p is an odd prime, i2 = j2 = k2 = p 1 and ij = (p 1)ji = k. The quaternion rings over Zp decompose into two parts form Zp + iZp(or Zp + jZp or Zp +kZp) with idempotent coe cients, depending on selecting a central orthogonal idempotent pair. The structures of cyclic and-constacyclic codes over Hp are determined, where p 3(mod 4), p is an odd prime, is a unit in Hp and some examples are given. The duals of linear codes over Hp are investigated. The parameters of quantum codes are obtained from cyclic codes and-constacyclic over Hp.

Event-based structured light (SL) systems leverage a novel neuromorphic sensor, the event camera, to realize high-speed, high dynamic range, and low power consumption depth sensing. In this field, the spatial coding method, e.g., random speckle, offers the highest scanning speed but has moderate reconstruction quality, whereas point or line scanning methods provide higher accuracy but are more time-consuming. To boost accuracy while maintaining efficiency, we design a novel cyclic spatial coding strategy for event-based SL systems, which embeds geometric constraints among multiple consecutive frames through the cyclic displacement of the random speckles. By exploiting the embedded geometric constraint, we further develop a geometric prior-guided stereo matching algorithm to achieve high-accuracy depth reconstruction. Additionally, we propose a multi-frame enhancing strategy to improve the quality of event frames, providing a robust basis for the stereo matching. Experiments demonstrate that the proposed method effectively boosts the performance of event-based SL systems, achieving high-accuracy 3D sensing at 1000 FPS.

Several classes of optimal ternary cyclic codes with two zeros

Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring R=GR(p2,m)[u], where u2=0 and pu=0. We first determine the algebraic structure of cyclic codes of arbitrary length n. For the case gcd(n,p)=1, we explicitly describe the generators of cyclic codes over R. Moreover, we establish necessary and sufficient conditions for the existence of self-dual and LCD codes, together with their enumeration. Several illustrative examples and tables are presented, highlighting the mass formula for cyclic self-orthogonal codes, cyclic LCD codes, and families of new cyclic codes that arise from our results.

New constructions of cyclic constant-dimension subspace codes based on Sidon spaces and subspace polynomials

New QEC codes from cyclic codes over finite chain rings

Quantum codes derived from constacyclic codes over Z3 [u,v

Linear recurring sequences and weight distributions of some cyclic codes

Abstract Given $${{\mathbb {F}}}_q$$ F q the finite field of size q, a flag code on $${{\mathbb {F}}}_q^n$$ F q n consists of a set of flags with a fixed sequence of dimensions (the type). In this paper, we deal with cyclic orbit flag codes, that are orbits of a Singer cycle of the general linear group acting on flags on $${{\mathbb {F}}}_q^n$$ F q n . Inspired by the results in Gluesing-Luerssen and Lehmann (Des Codes Crypt 89:447–470, 2021) and Roth et al. (IEEE Trans Inf Theory 64(6):4412–4422, 2018) about cyclic orbit codes, we completely characterize those cyclic orbit flag codes attaining the best distance for the largest possible orbit size, that is, optimal full-length cyclic orbit flag codes. Finally, we show that the distance distribution of this family of codes depends only on q, n and the type of the generating flag, also addressing the case of a union of orbits.

Let [Formula: see text] be a finite field of order [Formula: see text] and [Formula: see text] be a prime such that [Formula: see text] where [Formula: see text] are distinct odd primes with [Formula: see text] and [Formula: see text] is a positive integer with [Formula: see text]. In 2022, Rakphon et al. obtained all irreducible divisors of [Formula: see text] over [Formula: see text] where [Formula: see text] and [Formula: see text]. In this paper, we determine all primitive idempotents which can generate [Formula: see text]-constacyclic codes in [Formula: see text] where parity-check polynomials of these codes are shown in 2022. Moreover, we find the minimum Hammimg distances of the codes which are generated by primitive idempotents when [Formula: see text].

An infinite class of quantum codes derived from duadic constacyclic codes

Several classes of optimal quinary cyclic codes with minimum distance four

Multi-image encryption based on new two-dimensional hyperchaotic model via cyclic shift coding of deoxyribonucleic acid

Quantum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math> cyclic codes for biased noise

In telecommunications systems and networks designed for information transmission, independent and packet errors may occur simultaneously. To correct this type of error, it is advisable to use a code that can correct both packet and independent errors. Compound codes are one type of cyclic code. They are a type of systematic code. They are uniform, divisible, and block-based. They have an exceptional property: if a code combination belongs to a code, then a new combination obtained by cyclic permutation of bits also belongs to that code. These codes have a simple hardware implementation of encoding/decoding schemes and high efficiency in detecting and correcting errors. This, in turn, has ensured their widespread use. Irreducible polynomials are used to construct cyclic codes. To obtain a compound code, it is necessary to multiply the generating polynomial of the Fire code by the generating polynomial of the Bose-Chaudhuri-Hocquenghem (BCH) code. In reference literature, compound codes are usually denoted as FxBCH. A comparison of codes that correct only error packets and compound codes showed that compound codes have a greater number of check digits. Most of the obtained optimal compound codes can be used in practice in coding systems. The article studies compound codes that combine several coding methods to improve the reliability of data transmission in telecommunications systems. Their structure, advantages, and disadvantages compared to traditional codes, such as Hamming and Reed-Solomon codes, are considered. The effectiveness of compound codes in noisy channels is analyzed, including numerical calculations of error probabilities and performance comparisons. The results are presented in tables and graphs showing the dependence of effectiveness on channel parameters. The work aims to determine the optimal conditions for the use of compound codes in modern telecommunications systems, particularly in the context of 5G and promising 6G technologies.

The guessing number of a digraph is a new invariant in graph theory raised by S. Riis in 2006 and based on its applications in network coding and boolean circuit complexity theory. In this paper, we present the lower and upper bounds on a guessing number and linear guessing number of circulant digraphs by using cyclic codes. As an application of the lower bound, we construct a series of circulant digraphs with a larger linear guessing number and smaller degree. All of these circulant digraphs provide negative answers to S. Riis’ two open problems on the guessing number proposed in [Proceedings of the 2006 4th International Symposium on Modeling and Optimization in Mobile]. We also give a method to construct circulant digraphs with good estimation on their (linear) guessing number from cyclic codes.