Linear Skew Cyclic Codes over 𝔽qS

Abstract

In this study, we focus on skew cyclic codes over the family of rings 𝔽q S where q is a power of a prime number and S = 𝔽q + v𝔽q with v2 = v. Structural properties of these codes are studied in detail. Obtained results lead us to characterize 𝔽q S-linear skew cyclic codes. All the minimal spanning sets and generators of these codes are presented. Furthermore, some good 𝔽q -linear codes are obtained as images of the 𝔽q S-linear skew cyclic codes under the Gray mapping.

Keywords

• codes over rings
• gray map
• linear codes
• mixed alphabets
• skew polynomial rings
• 94b05
• 94b15