Weight distributions of generalized quasi-cyclic codes over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mi>u</mml:mi><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>

Gao, Jian; Meng, Xiangrui; Fu, Fang-Wei

doi:10.1016/j.ffa.2023.102181

Cited by 3 publications

(2 citation statements)

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“…Then, B β is a cyclic code of length 10 on P and its Gray image have the parameters [30,26,3] 5 over F 5 . Next, let us consider that κ 10 − 1 = (κ + 1) 5…”

Section: Applicationsmentioning

confidence: 99%

“…In recent years, there has been a rapid expansion of research on cyclic codes over finite rings, following the notable work of Hammons et al [3]. The literature extensively delves into the exploration of cyclic codes and their constructions across various finite rings, such as applications in constructing minimal codes in [4] and projective two-weight codes in [5]. Recently, Pereira and Mancini have given a general method to construct EAQEC codes from cyclic codes in [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Optimal and Quantum Code Construction from Cyclic Codes over FqPQ with Applications

Ali

Alali

Sharma

et al. 2023

Entropy

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The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive integer and p is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring P, we obtain several optimal codes with the help of the Gray image of cyclic codes.

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“…Then, B β is a cyclic code of length 10 on P and its Gray image have the parameters [30,26,3] 5 over F 5 . Next, let us consider that κ 10 − 1 = (κ + 1) 5…”

Section: Applicationsmentioning

confidence: 99%