Doubly-periodic sequences and a class of two-dimensional cyclic codes
type: Item
instance of: scholarly article
title: Doubly-periodic sequences and a class of two-dimensional cyclic codes
zbMATH Open document ID: 0765.16011
DOI: 10.1016/0196-8858(92)90003-F
published in: Advances in Applied Mathematics
publication date: 1992-09-26T00:00:00Z
review text: The main result of this paper is the following: The set of eventually doubly-periodic sequences over a finite field (as a Hopf algebra) is isomorphic to the tensor product of the space of eventually periodic sequences with itself. As a consequence of this result, the authors are able to extend their results to show that over any finite field, the space of double-periodic solutions to a double recurrence is isomorphic (as a coalgebra) to the sum of tensor products of solution space of associated single index recurrences. Also, it is shown that a standard construction of a 2-dimensional cyclic product code has an induced coalgebra structure. Some interesting open problems are presented at the end of the paper.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 56226
zbMATH Keywords: eventually doubly-periodic sequences
zbMATH Keywords: finite field
zbMATH Keywords: Hopf algebra
zbMATH Keywords: coalgebra
zbMATH Keywords: sum of tensor products
zbMATH Keywords: index recurrences
zbMATH Keywords: cyclic product code
author: Jerry I. Goldman
author: S. Homer
reviewed by: Joseph J. Liang
MaRDI profile type: Publication
cites work: Algebraic coding theory
cites work: Cyclic product codes
cites work: Doubly-Periodic Sequences and Two-Dimensional Recurrences
cites work: Binary Codes Which Are Ideals in the Group Algebra of an Abelian Group
cites work: The Hopf algebra of linearly recursive sequences
cites work: General theory of doubly periodic arrays over an arbitrary finite field and its applications
cites work: On determining the independent point set for doubly periodic arrays and encoding two-dimensional cyclic codes and their duals
cites work: Q5590089
cites work: Linear Recurring Sequences
full work available at URL: 0196-8858(92)90003-f
OpenAlex ID: W2019936531
description: scientific article; zbMATH DE number 56226