Cyclic and constacyclic codes over the ring Z4[u]/⟨u3 − u2⟩ and their Gray images
نویسندگان
چکیده
منابع مشابه
On constacyclic codes over Z4[u]/〈u2-1〉 and their Gray images
We first define a new Gray map from R = Z4+uZ4 to Z 2 4, where u 2 = 1 and study (1 + 2u)-constacyclic codes over R. Also of interest are some properties of (1 + 2u)constacyclic codes over R. Considering their Z4 images, we prove that the Gray images of (1+2u)-constacyclic codes of length n over R are cyclic codes of length 2n over Z4. In many cases the latter codes have better parameters than ...
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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 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 ...
متن کاملOn Skew Cyclic Codes over a Finite Ring
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.
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2021
ISSN: 1303-6149
DOI: 10.3906/mat-2006-112