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- Title
On some skew codes over ℤq+uℤq.
- Authors
Hebbache, Zineb; Kaya, Abidin; Aydin, Nuh; Guenda, Kenza
- Abstract
In this paper, we investigate the structure and properties of skew negacyclic codes and skew quasi-negacyclic codes over the ring R = ℤ q + u ℤ q , u 2 = 0. Some structural properties of R [ x , Θ ] are discussed, where Θ is an automorphism of R. A skew quasi-negacyclic code of length s ℓ with index ℓ over R is viewed both as in the conventional row circulant form and also as an R [ x , Θ ] / (x s + 1) -submodule of G R (R , ℓ) [ x , δ ] / (x s + 1) , where G R (R , ℓ) is the Galois extension ring of degree ℓ over R and δ is an automorphism of G R (R , ℓ). A sufficient condition for one generator skew quasi-negacyclic codes to be free is determined. Some distance bounds for free one generator skew quasi-negacyclic codes are discussed. Furthermore, given the decomposition of a skew quasi-negacyclic code, we provide the decomposition of its dual code. As a result, a characterization of self-dual skew quasi-negacyclic codes over R = ℤ q + u ℤ q is provided. By using computer search we obtained a number of new linear codes over ℤ 4 from skew negacyclic and skew quasi-negacyclic codes over ℤ 4 + u ℤ 4 .
- Subjects
LINEAR codes; ELECTRONIC information resource searching; DATABASE searching; POLYNOMIAL rings
- Publication
Discrete Mathematics, Algorithms & Applications, 2024, Vol 16, Issue 1, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830922501865