Information Rates and Weights of Codes in Structural Matrix Rings

Authors:
Andrei Kelarev;Olga Sokratova
Affiliations:
-;-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

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Abstract

Several efficient error-correcting codes are ideals in certain ring constructions. We consider two-sided ideals in structural matrix rings defined in terms of directed graphs with the set of vertices corresponding to rows and columns, and with edges corresponding to nonzero entries in matrices of the ring. Formulas for Hamming weights of all ideals in structural matrix rings are found and sharp upper bounds for information rates of these ideals are given.