Cyclic and some constacyclic codes over the ring Z4[u]〈u2−1〉
نویسندگان
چکیده
منابع مشابه
Cyclic and constacyclic codes over a non-chain ring
In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/〈v − v〉 where p is a prime. This is a generalization of the case p = 3. Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlighte...
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Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
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Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
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In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
متن کاملSome constacyclic codes over finite chain rings
For λ an n-th power of a unit in a finite chain ring we prove that λ-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the α+pβconstacyclic codes of length p over the Galois ring GR(p, r).
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2016
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2015.12.003