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- Title
Characterizations and Properties of Monic Principal Skew Codes over Rings.
- Authors
Boulagouaz, Mhammed; Deajim, Abdulaziz
- Abstract
Let A be a ring with identity, σ a ring endomorphism of A that maps the identity to itself, δ a σ -derivation of A , and consider the skew-polynomial ring A X ; σ , δ . When A is a finite field, a Galois ring, or a general ring, some fairly recent literature used A X ; σ , δ to construct new interesting codes (e.g., skew-cyclic and skew-constacyclic codes) that generalize their classical counterparts over finite fields (e.g., cyclic and constacyclic linear codes). This paper presents results concerning monic principal skew codes, called herein monic principal f , σ , δ -codes, where f ∈ A X ; σ , δ is monic. We provide recursive formulas that compute the entries of both a generator matrix and a control matrix of such a code C. When A is a finite commutative ring and σ is a ring automorphism of A , we also give recursive formulas for the entries of a parity-check matrix of C. Also, in this case, with δ = 0 , we present a characterization of monic principal σ -codes whose dual codes are also monic principal σ -codes, and we deduce a characterization of self-dual monic principal σ -codes. Some corollaries concerning monic principal σ -constacyclic codes are also given, and a good number of highlighting examples is provided.
- Subjects
FINITE rings; PARITY-check matrix; FINITE fields; COMMUTATIVE rings; ENDOMORPHISM rings; CYCLIC codes; BINARY codes; POLYNOMIAL rings
- Publication
Security & Communication Networks, 2022, p1
- ISSN
1939-0114
- Publication type
Article
- DOI
10.1155/2022/9294459