We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
(β , γ)-Skew QC Codes with Derivation over a Semi-Local Ring.
- Authors
Ashraf, Mohammad; Alali, Amal S.; Asim, Mohd; Mohammad, Ghulam
- Abstract
In this article, we consider a semi-local ring S = F q + u F q , where u 2 = u , q = p s and p is a prime number. We define a multiplication y b = β (b) y + γ (b) , where β is an automorphism and γ is a β -derivation on S so that S [ y ; β , γ ] becomes a non-commutative ring which is known as skew polynomial ring. We give the characterization of S [ y ; β , γ ] and obtain the most striking results that are better than previous findings. We also determine the structural properties of 1-generator skew cyclic and skew-quasi cyclic codes. Further, We demonstrate remarkable results of the above-mentioned codes over S. Finally, we find the duality of skew cyclic and skew-quasi cyclic codes using a symmetric inner product. These codes are further generalized to double skew cyclic and skew quasi cyclic codes and a table of optimal codes is calculated by MAGMA software.
- Subjects
CYCLIC codes; NONCOMMUTATIVE rings; POLYNOMIAL rings; PRIME numbers; LAURENT series
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 1, p225
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15010225