A circulant approach to skew-constacyclic codes

作者：Fogarty Neville; Guesing Luerssen Heide^*

来源：Finite Fields and Their Applications, 2015, 35: 92-114.

DOI：10.1016/j.ffa.2015.03.008

• Linear block codes
• Skew-cyclic codes
• Skew-polynomial rings
• Circulants

We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;theta] modulo the left ideal generated by a polynomial of the form x(n) - a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where x(n) - a is central.

• 出版日期2015-9