Cyclic codes over a non-chain ring R, and their application to LCD codes

2021 ◽  
Vol 344 (10) ◽  
pp. 112545
Author(s):  
Habibul Islam ◽  
Edgar Martínez-Moro ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Chain Ring ◽  
Lcd Codes

scholarly journals New Quantum and LCD Codes over Finite Fields of Even Characteristic

2021 ◽  
Vol 71 (5) ◽  
pp. 656-661
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Finite Fields ◽  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Gray Map ◽  
Chain Ring ◽  
Lcd Codes ◽  
Lcd Code ◽  
Quantum Error

For an integer m ≥ 1, we study cyclic codes of length l over a commutative non-chain ring F2m + uF2m , where u2 = u . With a new Gray map and Euclidean dual-containing cyclic codes, we provide many new and superior codes to the best-known quantum error-correcting codes. Also, we characterise LCD codes of length l with respect to their generator polynomials and prove that F2m − image of an LCD code of length l is an LCD code of length 2l . Finally, we provide several optimal LCD codes from the Gray images of LCD codes over F2m + uF2m .  

scholarly journals Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

2020 ◽  
Vol 70 (6) ◽  
pp. 626-632
Author(s):  
Om Prakash ◽  
Shikha Yadav ◽  
Ram Krishna Verma
Keyword(s):  
Cyclic Codes ◽  
Gray Map ◽  
Constacyclic Codes ◽  
Dual Codes ◽  
Gray Image ◽  
New Class ◽  
Sharing Scheme ◽  
Lcd Codes ◽  
Reversible Cyclic Codes

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

Hermitian LCD codes from cyclic codes

2017 ◽  
Vol 86 (10) ◽  
pp. 2261-2278 ◽  
Author(s):  
Chengju Li
Keyword(s):  
Cyclic Codes ◽  
Lcd Codes

Linear codes from vectorial Boolean functions in the context of algebraic attacks

2020 ◽  
pp. 2150032
Author(s):  
M. Boumezbeur ◽  
S. Mesnager ◽  
K. Guenda
Keyword(s):  
Boolean Functions ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Weight Enumerator ◽  
Direct Link ◽  
Algebraic Attacks ◽  
Vectorial Boolean Functions ◽  
Lcd Codes ◽  
Vectorial Function ◽  
The Relationship

In this paper, we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain [Formula: see text]-ary cyclic codes (which we show that they are LCD codes). We also present some properties of those cyclic codes as well as their weight enumerator. In addition, we generalize the so-called algebraic complement and study its properties.

Skew Cyclic Codes over a Non-chain Ring

2017 ◽  
Vol 26 (3) ◽  
pp. 544-547 ◽  
Author(s):  
Minjia Shi ◽  
Ting Yao ◽  
Patrick Solé
Keyword(s):  
Cyclic Codes ◽  
Chain Ring ◽  
Skew Cyclic Codes

scholarly journals On the Structure of Cyclic Codes Over $\mathbb{F}_{q}{RS}$ and Applications in Quantum and LCD Codes Constructions

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 18902-18914 ◽  
Author(s):  
Hai Q. Dinh ◽  
Tushar Bag ◽  
Ashish Kumar Upadhyay ◽  
Ramakrishna Bandi ◽  
Warattaya Chinnakum
Keyword(s):  
Cyclic Codes ◽  
Lcd Codes

On Cyclic and Negacyclic Codes of Length 8ps Over Fpm + uFpm

2020 ◽  
Vol 87 (3-4) ◽  
pp. 231
Author(s):  
Saroj Rani
Keyword(s):  
Positive Integer ◽  
Algebraic Structure ◽  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Chain Ring ◽  
Negacyclic Codes

In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over the chain ring Fp<sup>m</sup> + uFp<sup>m</sup> in terms of their generator polynomials, where u<sup>2</sup> = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>. Also, we determine μ and -constacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>.

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