On the structure of repeated-root polycyclic codes over local rings

DOI10.1016/j.disc.2023.113715arXiv2208.00512MaRDI QIDQ6056443

Edgar Martínez-Moro, Maryam Bajalan, Gülsüm Gözde Yılmazgüç, R. Sobhani, Steve Szabo

Publication date: 30 October 2023

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

Full work available at URL: https://arxiv.org/abs/2208.00512

zbMATH Keywords

duality matrix-product code repeated-root code Mattson-Solomon transform polycyclic code

Mathematics Subject Classification ID

Cyclic codes (94B15)

Cites Work

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Matrix-product structure of repeated-root cyclic codes over finite fields
On a class of repeated-root monomial-like abelian codes
On the duality and the direction of polycyclic codes
A class of optimal \(p\)-ary codes from one-weight codes over \(\mathbb F_p[u/\langle u^m\rangle\)]
Two and three weight codes over \(\mathbb {F}_p+u\mathbb {F}_p\)
Homogeneous weights of matrix product codes over finite principal ideal rings
On quasi-twisted codes over finite fields
Matrix-product codes over finite chain rings
On the structure of linear and cyclic codes over a finite chain ring
On the key equation over a commutative ring
Matrix-product structure of constacyclic codes over finite chain rings \(\mathbb{F}_{p^m}[u/\langle u^e\rangle\)]
Finite local rings
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
Homogeneous metric and matrix product codes over finite commutative principal ideal rings
Polycyclic codes as invariant subspaces
A transform approach to polycyclic and serial codes over rings
On polycyclic codes over a finite chain ring
Dual generalizations of the concept of cyclicity of codes
On matrix-product structure of repeated-root constacyclic codes over finite fields
Commutative algebra: constructive methods. Finite projective modules. Translated from the French by Tania K. Roblot
Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over \(\mathbb{F}_4\)
On trace codes and Galois invariance over finite commutative chain rings
Matrix product codes over finite commutative Frobenius rings
On the algebraic structure of quasi-cyclic codes. IV: Repeated roots
The Generalized Vandermonde Matrix
Linear Complexity of Periodic Sequences: A General Theory
Cyclic and Negacyclic Codes Over Finite Chain Rings
On the algebraic structure of quasi-cyclic codes .I. Finite fields
Multivariable Codes Over Finite Chain Rings: Serial Codes
Matrix-product codes over \(\mathbb{F}_q\)

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