On matrix-product structure of repeated-root constacyclic codes over finite fields

DOI10.1016/j.disc.2019.111768zbMath1442.94058arXiv1705.08819OpenAlexW2998120784MaRDI QIDQ2297724

Paravee Maneejuk, Yuan Cao, Yong-Lin Cao, Fang-Wei Fu, Hai Quang Dinh

Publication date: 20 February 2020

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.08819

zbMATH Keywords

finite chain ringmatrix-product codemonomially equivalent codesrepeated-root constacyclic code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15)

Related Items (11)

Constacyclic codes of length \(8p^s\) over \(\mathbb{F}_{p^m} + u\mathbb{F}_{p^m}\) ⋮ On \(\mathbb{F}_2 RS\)-cyclic codes and their applications in constructing optimal codes ⋮ On constacyclic codes of length \(p^s\) over \(\mathbb{F}_{p^m} [ u , v \slash \langle u^2 , v^2 , u v - v u \rangle \)] ⋮ On the structure of repeated-root polycyclic codes over local rings ⋮ New quantum codes from matrix-product codes over small fields ⋮ Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length \(3p^s\) ⋮ MDS constacyclic codes of prime power lengths over finite fields and construction of quantum MDS codes ⋮ Hamming distances of constacyclic codes of length \(3p^s\) and optimal codes with respect to the Griesmer and Singleton bounds ⋮ Constructing MDS Galois self-dual constacyclic codes over finite fields ⋮ New stabilizer codes from the construction of dual-containing matrix-product codes ⋮ Hamming distance of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m} \)

Cites Work

• Unnamed Item
• Unnamed Item
• Repeated-root constacyclic codes of prime power length over \(\frac{\mathbb{F}_{p^m} [u}{\langle u^a \rangle}\) and their duals]
• Matrix-product structure of repeated-root cyclic codes over finite fields
• New linear codes from matrix-product codes with polynomial units
• A class of constacyclic codes over a finite field
• Construction and decoding of matrix-product codes from nested codes
• Matrix-product codes over finite chain rings
• On the algebraic structure of quasi-cyclic codes. II: Chain rings
• A propagation rule for linear codes
• On the structure of linear and cyclic codes over a finite chain ring
• Note on Niederreiter-Xing's propagation rule for linear codes
• Type 2 constacyclic codes over \(\mathbb{F}_{2^m} [u \slash \langle u^3 \rangle\) of oddly even length]
• Matrix-product structure of constacyclic codes over finite chain rings \(\mathbb{F}_{p^m}[u/\langle u^e\rangle\)]
• A class of repeated-root constacyclic codes over \(\mathbb{F}_{p^m} [u / \langle u^e \rangle\) of type 2]
• On the Hamming distances of repeated-root constacyclic codes of length \(4p^s\)
• List decoding of matrix-product codes from nested codes: an application to quasi-cyclic codes
• Construction and enumeration for self-dual cyclic codes of even length over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \)
• On the symbol-pair distances of repeated-root constacyclic codes of length \(2 p^s\)
• Structure of some classes of repeated-root constacyclic codes of length \(2^{\mathfrak{K}} \ell^m p^n\)
• An explicit representation and enumeration for self-dual cyclic codes over \(\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}\) of length \(2^s\)
• On constacyclic codes over finite chain rings
• Matrix product codes over finite commutative Frobenius rings
• A class of linear codes of length 2 over finite chain rings
• A Generalization of Niederreiter–Xing's Propagation Rule and Its Commutativity With Duality
• Some ternary and quaternary codes and associated sphere packings
• On the minimum distance of ternary cyclic codes
• Duality for modules over finite rings and applications to coding theory
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Fundamentals of Error-Correcting Codes
• Constacyclic codes, cocycles and a u+v|u-v construction
• DECODING OF MATRIX-PRODUCT CODES
• Skew constacyclic codes over finite commutative semi-simple rings
• Optimal b-symbol constacyclic codes with respect to the Singleton bound
• MDS Symbol-Pair Cyclic Codes of Length $2p^s$ over $\mathbb F_{p^m}$
• On a Class of Constacyclic Codes of Length 4p^s over Fpm[u〈 ua 〉]
• Code equivalence characterizes finite Frobenius rings
• RT distance and weight distributions of Type 1 constacyclic codes of length 4ps over Fpm[u]
• Matrix-product codes over \(\mathbb{F}_q\)

This page was built for publication: On matrix-product structure of repeated-root constacyclic codes over finite fields