ℤ₂ℤ₄-Additive Quasi-Cyclic Codes

Shi, Minjia; Li, Shitao; Solé, Patrick

doi:10.1109/tit.2021.3111858

Cited by 10 publications

(3 citation statements)

References 25 publications

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“…Further, choosing g 3 (x) = x 2 + 1, f 3,0 (x) = x 7 + x 6 + x 5 + x 2 , and f 3,1 = x 9 + x 6 + x 5 + x 3 + 1; then, ([g 3 (x)f 3,0 ], [g 3 (x)f 3,1 ]) can also generate an symplectic LCD [20,8,6] (27, 4, ≥ 18) 4 ACD code, which is also performing better than LCD code [27,4,17] 4 in the literature [33].…”

Section: Bound On Symplectic Weight Of 1-generator Quasi-cyclic Codes...mentioning

confidence: 99%

“…Quasi-cyclic codes are an interesting class of linear codes that exhibit good performance in constructing new or recorded linear codes in [1]. With appropriate mappings established, quasicyclic code can be used to construct good additive codes [25], [26], [27], [28], [29]. However, there is still a lack of practical approaches to constructing additive codes using quasi-cyclic codes, which makes it challenging to construct good additive codes with quasi-cyclic codes.…”

Section: Introductionmentioning

confidence: 99%

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Some good quaternary additive codes outperform linear counterparts

Guan¹,

Li²,

Liu³

et al. 2023

Preprint

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It is well known that additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distance than linear codes of the same length and dimension. To advance this problem, this paper focuses on constructing additive codes that outperform linear codes using quasi-cyclic codes and combinatorial methods. Firstly, we propose a lower bound on the minimum symplectic distance of 1generator quasi-cyclic codes of index even. Further, we get many binary quasi-cyclic codes with large symplectic distances utilizing computer-supported combination and search methods, all corresponding to good quaternary additive codes. Notably, 15 additive codes have greater distances than best-known quaternary linear codes in Grassl's code table (bounds on the minimum distance of quaternary linear codes http://www.codetables.de) for the same lengths and dimensions. Moreover, employing a combinatorial approach, we partially determine the parameters of optimal quaternary additive 3.5-dimensional codes with lengths from 28 to 254. Finally, as an extension, we also construct some good additive complementary dual codes with larger distances than best-known quaternary linear complementary dual codes in the literature.

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Section: Bound On Symplectic Weight Of 1-generator Quasi-cyclic Codes...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some good quaternary additive codes outperform linear counterparts

Guan¹,

Li²,

Liu³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Two-dimensional (2D, for short) cyclic codes which have a long history, see for example [12,13], still gain attention, see [9-11, 22, 23] and the references therein. As mentioned in [9], these codes are special cases of quasi-cyclic codes which form an important and well-studied class of codes (see, for example, [1,3,7,18,21,25] and their references). Also constacyclic codes which are a generalization of cyclic codes are investigated over finite fields and some other types of rings, see [5,24] and their references.…”

Section: Introductionmentioning

confidence: 99%

One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

Khormaei¹,

Nikseresht²,

Namazi³

2022

Preprint

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In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field F = F q . We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual. Moreover, we prove that if there exists an asymptotically good family of one-sided repeated-root two-dimensional cyclic or constacyclic codes, then there exists an asymptotically good family of simple root two-dimensional cyclic or constacyclic codes with parameters at least as good as the first family. Furthermore, we show that several of the main results of the papers Rajabi and Khashyarmanesh (2018) [20] and Sepasdar and Khashyarmanesh (2016) [23] are not accurate and find other conditions needed for them to hold.

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Two classes of quasi-cyclic codes via irreducible polynomials

Huang

Yue

2023

Cryptogr. Commun.

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ℤ₂ℤ₄-Additive Quasi-Cyclic Codes

Cited by 10 publications

References 25 publications

Some good quaternary additive codes outperform linear counterparts

Some good quaternary additive codes outperform linear counterparts

One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

Two classes of quasi-cyclic codes via irreducible polynomials

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