Skew quasi cyclic codes over 𝔽q + v𝔽q

Abstract

In this work, skew quasi cyclic codes over [Formula: see text], where [Formula: see text] are considered. The generating set for one generator skew quasi cyclic codes over [Formula: see text] is also determined. We discuss a sufficient condition for one generator skew quasi cyclic codes to be free. Furthermore, a BCH type bound is given for free one generator skew quasi cyclic codes. We investigate the dual of skew quasi cyclic codes over [Formula: see text]. We give a necessary and sufficient condition for skew cyclic codes over [Formula: see text] to contain its dual. Moreover, we construct quantum codes from skew cyclic codes over [Formula: see text]. By using computer search we give some examples about skew quasi cyclic codes and list some quantum parameters in the table.

Quantum and LCD codes from Skew Constacyclic Codes over a General Class of Non-chain Rings

“…Motivated by these studies many researchers obtained quantum codes using cyclic and constacyclic codes which either contain their dual (dual-containing) or contained in their dual (self-orthogonal) over various chain and non-chain rings [2, 6-8, 10, 12, 12, 25-27, 30-32, 41-43, 48, 53, 57, 58, 68, 76, 80]. In 2019, Özen et al [61] derived the conditions for a skew cyclic code over F q to be self-orthogonal and dual-containing. Further a rectified version of this criterion was introduced by Bag et al in [11].…”