A class of linear codes of length over finite chain rings
Journal of Algebra and its Applications, 2020•World Scientific
Let 𝔽 pm be a finite field of cardinality pm, where p is an odd prime, k, λ be positive integers
satisfying λ≥ 2, and denote 𝒦= 𝔽 pm [x]/〈 f (x) λ pk〉, where f (x) is an irreducible
polynomial in 𝔽 pm [x]. In this note, for any fixed invertible element ω∈ 𝒦×, we present all
distinct linear codes S over 𝒦 of length 2 satisfying the condition:(ω f (x) pka 1, a 0)∈ S for all
(a 0, a 1)∈ S. This conclusion can be used to determine the structure of (δ+ α u 2)-
constacyclic codes over the finite chain ring 𝔽 pm [u]/〈 u 2 λ〉 of length npk for any positive …
satisfying λ≥ 2, and denote 𝒦= 𝔽 pm [x]/〈 f (x) λ pk〉, where f (x) is an irreducible
polynomial in 𝔽 pm [x]. In this note, for any fixed invertible element ω∈ 𝒦×, we present all
distinct linear codes S over 𝒦 of length 2 satisfying the condition:(ω f (x) pka 1, a 0)∈ S for all
(a 0, a 1)∈ S. This conclusion can be used to determine the structure of (δ+ α u 2)-
constacyclic codes over the finite chain ring 𝔽 pm [u]/〈 u 2 λ〉 of length npk for any positive …
Let be a finite field of cardinality , where is an odd prime, be positive integers satisfying , and denote , where is an irreducible polynomial in . In this note, for any fixed invertible element , we present all distinct linear codes over of length satisfying the condition: for all . This conclusion can be used to determine the structure of -constacyclic codes over the finite chain ring of length for any positive integer satisfying .
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