Counting Z2 Z4 Z8-additive Codes

Basri Çalışkan, Kemal Balıkçı

Abstract

In Algebraic Coding Theory, all linear codes are described by generator matrices. Any linear code has many generator matrices which are equivalent. It is important to find the number of the generator matrices for constructing of these codes. In this paper, we study Z_2 Z_4 Z_8-additive codes, which are the extension of recently introduced Z_2 Z_4-additive codes. We count the number of arbitrary Z_2 Z_4 Z_8-additive codes. Then we investigate connections to Z_2 Z_4 and Z_2 Z_8-additive codes with Z_2 Z_4 Z_8, and give some illustrative examples.

Keywords

Additive codes, Z_2 Z_4 Z_8-additive codes, Gaussian numbers.

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