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- W2892415281 abstract "Let $A$ be a ring with identity, $sigma$ a ring endomorphism of $A$ that maps the identity to itself, $delta$ a $sigma$-derivation of $A$, and consider the skew-polynomial ring $A[X;sigma,delta]$. When $A$ is a finite field, a Galois ring, or a general ring, some fairly recent literature used $A[X;sigma,delta]$ 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 {it principal} $(f, sigma, delta)$-codes over a ring $A$, where $fin A[X;sigma,delta]$ is monic. We provide recursive formulas that compute the entries of both a generating matrix and a control matrix of such a code $mathcal{C}$. When $A$ is a finite commutative ring with identity and $sigma$ is a ring automorphism of $A$, we also give recursive formulas for the entries of a parity-check matrix of $mathcal{C}$. Also in this case, with $delta=0$, we give a generating matrix of the dual $mathcal{C}^perp$, present a characterization of principal $sigma$-codes whose duals are also principal $sigma$-codes, and deduce a characterization of self-dual principal $sigma$-codes. Some corollaries concerning principal $sigma$-constacyclic codes are also given, and some highlighting examples are provided." @default.
- W2892415281 created "2018-10-05" @default.
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- W2892415281 date "2018-09-27" @default.
- W2892415281 modified "2023-09-27" @default.
- W2892415281 title "On Principal $(f, sigma, delta)$-Codes over Rings" @default.
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