On the construction of nonbinary LCD quadratic residue and double quadratic residue codes

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2025-02-11 DOI:10.1016/j.ffa.2025.102591

Arezoo Soufi Karbaski , Taher Abualrub , Irfan Siap , Hashem Bordbar

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引用次数: 0

Abstract

Linear complementary dual (LCD) codes are an important class of error-correcting codes because of their applications in many areas such as their applications in cryptography and secret sharing [1], [4], [7]. In this paper, we construct a large class of nonbinary LCD codes from the class of nonbinary quadratic residue (QR) codes and nonbinary double QR codes. We have also introduced the class of extended quasi quadratic residue (QQR) codes and construct self-orthogonal codes from these codes. As an application of our study, we have presented an optimal ternary self-orthogonal code of parameters

[24, 6, 12]

. We have also constructed examples of self-orthogonal codes with parameters

{[2 (q + 1), \frac{q + 1}{2}, 2 d]}_{p}

and also examples of LCD codes with parameters

{[2 q, \frac{q - 1}{2}, 2 d]}_{p}

and

{[2 q, \frac{q + 1}{2}, 2 d]}_{p}

over

F_{p}

for different values of primes p and q.

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.

期刊最新文献

Permutation polynomials of the form xrh(xq−1) over Fq2 with even characteristics Some results on linear subspace codes Four families of q-ary self-orthogonal codes via the defining-set construction On the construction of nonbinary LCD quadratic residue and double quadratic residue codes Homogenization of binary linear codes and their applications