Skew Generalized Quasi-Cyclic Codes over Finite Fields

Abstract

In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynomial, determine the dimension and give a lower bound on the minimum Hamming distance. The skew quasi-cyclic (QC) codes are also discussed briefly.

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Cited by in corpus (2)

• On the codes over the Z_3+vZ_3+v^2Z_3
• Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$