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Abstract
In this paper, we study the algebraic structure of -additive codes which are
-submodules where
is prime, and
and
are positive integers.
-additive codes naturally generalize
and
-additive codes which have been introduced recently. The results obtained in this work generalize a great amount of the studies done on additive codes. Especially, we determine the standard forms of generator and parity-check matrices for this family of codes. This leads to the identification of the type and the cardinalities of these codes. Furthermore, we present some bounds on the minimum distance and examples that attain these bounds. Finally, we present some illustrative examples for some special cases.
AMS Subject Classifications:
Acknowledgement
The authors wish to express their thanks to the anonymous referees whose remarks and suggestions greatly improved the paper.