Constacyclic Codes of Length 3p s Over F p m + uF p m and Their Application in Various Distance Distributions
نویسندگان
چکیده
منابع مشابه
Constacyclic codes of length $4p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$
Let p be an odd prime, s,m be positive integers and Fpm be the finite field with p m elements. In this paper, we determine all constacyclic codes of length 4p over the finite commutative chain ring R = Fpm + uFpm with unity, where u 2 = 0. We also determine their dual codes and list some isodual constacyclic codes of length 4p over R.
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Let Fpm be a finite field of cardinality p m and R = Fpm[u]/〈u 〉 = Fpm +uFpm (u = 0), where p is a prime and m is a positive integer. For any λ ∈ Fpm, an explicit representation for all distinct λ-constacyclic codes over R of length pn is given by a canonical form decomposition for each code, where s and n are positive integers satisfying gcd(p, n) = 1. For any such code, using its canonical fo...
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For any prime p, λ-constacyclic codes of length p over R = Fpm + uFpm are precisely the ideals of the local ring Rλ = R[x] 〈xp−λ〉 , where u = 0. In this paper, we first investigate the Hamming distances of cyclic codes of length p over R. The minimum Hamming distances of all cyclic codes of length p over R are determined. Moreover, an isometry between cyclic and α-constacyclic codes of length p...
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We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengt...
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ژورنال
عنوان ژورنال: IEEE Access
سال: 2020
ISSN: 2169-3536
DOI: 10.1109/access.2020.3036158