Doubly-periodic sequences and a class of two-dimensional cyclic codes
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.
scientific article; zbMATH DE number 56226