Cyclic codes over a non-chain ring \(R_{e,q}\) and their application to LCD codes
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Publication:2043406
DOI10.1016/j.disc.2021.112545zbMath1476.94048arXiv2106.07962OpenAlexW3185223764MaRDI QIDQ2043406
Om Prakash, Habibul Islam, Edgar Martínez-Moro
Publication date: 2 August 2021
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.07962
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Cyclic codes (94B15) Structure of finite commutative rings (13M05)
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Uses Software
Cites Work
- Complementary dual codes for counter-measures to side-channel attacks
- Cyclic and constacyclic codes over a non-chain ring
- A class of skew-constacyclic codes over \(\mathbb{Z}_{4} + u \mathbb{Z}_{4}\)
- On complementary-dual quasi-cyclic codes
- Linear codes with complementary duals
- Cyclic codes over the integers modulo \(p^m\).
- Cyclic self-dual \(\mathbb Z_4\)-codes.
- The condition for a cyclic code to have a complementary dual
- The combinatorics of LCD codes: linear programming bound and orthogonal matrices
- Codes over affine algebras with a finite commutative chain coefficient ring
- Some bounds on binary LCD codes
- Cyclic codes and \(\lambda_1 + \lambda_2 u + \lambda_3 v + \lambda_4 u v\)-constacyclic codes over \(\mathbb{F}_p + u \mathbb{F}_p + v \mathbb{F}_p + u v \mathbb{F}_p\)
- Cyclic codes over \(\mathbb{Z}_{4}\) of oddly even length.
- Linear codes with complementary duals meet the Gilbert-Varshamov bound
- A study of cyclic and constacyclic codes over \(\mathbb Z_{4} + u\mathbb Z_{4} + v\mathbb Z_{4}\)
- New \(\mathbb{Z}_4\) codes from constacyclic codes over a non-chain ring
- Self-dual and LCD double circulant and double negacirculant codes over \({\mathbb{F}}_q+u{\mathbb{F}}_q+v{\mathbb{F}}_q\)
- Do non-free LCD codes over finite commutative Frobenius rings exist?
- \(\sigma\)-LCD codes over finite chain rings
- LCD codes over finite chain rings
- Some results on linear codes over \(\mathbb {F}_p+u\mathbb {F}_p+u^2\mathbb {F}_p\)
- Cyclic codes over the rings \(\mathbb Z_2 + u\mathbb Z_2\) and \(\mathbb Z_2 + u\mathbb Z_2 + u^2 \mathbb Z_2\)
- ON LCD CODES OVER FINITE CHAIN RINGS
- A Mass Formula and Rank of<tex>$BBZ_4$</tex>Cyclic Codes of Length<tex>$2^e$</tex>
- Cyclic and Negacyclic Codes Over Finite Chain Rings
- Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/
- A class of constacyclic codes over the ring Z4[u,v/<u2,v2,uv - vu> and their Gray images]
- Topics in Galois Fields
- Some Results on Cyclic Codes Over ${F}_{2}+v{F}_{2}$
- LCD Cyclic Codes Over Finite Fields