Codes over affine algebras with a finite commutative chain coefficient ring

DOI10.1016/j.ffa.2017.09.008zbMath1430.94104arXiv1709.05464OpenAlexW2962911905MaRDI QIDQ1679699

A. Piñera-Nicolás, Edgar Martínez-Moro, Ignacio F. Rúa

Publication date: 21 November 2017

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.05464

zbMATH Keywords

quasi-cyclic codesaffine algebramultivariable codesfinite commutative chain ringcodes over non-chain local Frobenius rings

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Other types of codes (94B60) Cyclic codes (94B15) Polynomials and finite commutative rings (13M10) Quantum coding (general) (81P70)

Related Items (5)

On polycyclic codes over a finite chain ring ⋮ On cyclic codes over \(\mathbb{Z}_q [u / \langle u^2 \rangle\) and their enumeration] ⋮ Infinite families of MDR cyclic codes over \(\mathbb{Z}_4\) via constacyclic codes over \(\mathbb{Z}_4 [u \slash \langle u^2 - 1 \rangle \)] ⋮ Cyclic codes over a non-chain ring \(R_{e,q}\) and their application to LCD codes ⋮ On \(\mathbb{Z}_2\mathbb{Z}_4\)-additive polycyclic codes and their Gray images

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Codes over \(R_k\), Gray maps and their binary images
• On repeated-root multivariable codes over a finite chain ring
• On the algebraic structure of quasi-cyclic codes. II: Chain rings
• On the structure of linear and cyclic codes over a finite chain ring
• Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
• 1-generator quasi-cyclic codes over finite chain rings
• Quasi-abelian codes
• Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over \(\mathbb{F}_4\)
• Codes over finite quotients of polynomial rings
• Bounds on quasi-cyclic codes over finite chain rings
• Cyclic and Negacyclic Codes Over Finite Chain Rings
• Canonical generating system of a monic polynomial ideal over a commutative Artinian chain ring
• Linearly representable codes and the Kerdock code over an arbitrary Galois field of characteristic 2
• Multivariable Codes Over Finite Chain Rings: Serial Codes
• Algebraic structure of quasicyclic codes

This page was built for publication: Codes over affine algebras with a finite commutative chain coefficient ring