Characterizations and Properties of Monic Principal Skew Codes over Rings
نویسندگان
چکیده
Let A be a ring with identity, id="M2"> σ endomorphism of id="M3"> that maps the identity to itself, id="M4"> δ id="M5"> -derivation id="M6"> , and consider skew-polynomial id="M7"> X ; , . When id="M8"> is finite field, Galois ring, or general some fairly recent literature used id="M9"> construct new interesting codes (e.g., skew-cyclic skew-constacyclic codes) generalize their classical counterparts over fields cyclic constacyclic linear codes). This paper presents results concerning monic principal skew codes, called herein id="M10"> open="(" close=")" f -codes, where id="M11"> ∈ monic. We provide recursive formulas compute entries both generator matrix control such code id="M12"> C id="M13"> commutative id="M14"> automorphism id="M15"> we also give for parity-check id="M16"> Also, in this case, id="M17"> = 0 present characterization id="M18"> -codes whose dual are id="M19"> deduce self-dual id="M20"> -codes. Some corollaries id="M21"> -constacyclic given, good number highlighting examples provided.
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ژورنال
عنوان ژورنال: Security and Communication Networks
سال: 2022
ISSN: ['1939-0122', '1939-0114']
DOI: https://doi.org/10.1155/2022/9294459