A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

A study of constacyclic codes over the ring ℤ4[u]/〈u2 − 3〉

2018 ◽  
Vol 10 (04) ◽  
pp. 1850056
Author(s):  
Tushar Bag ◽  
Habibul Islam ◽  
Om Prakash ◽  
Ashish K. Upadhyay
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study [Formula: see text]-constacyclic codes over the ring [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], respectively. We define some new Gray maps from [Formula: see text] to the copies of [Formula: see text]. It is shown that Gray images of [Formula: see text]-constacyclic codes over [Formula: see text] are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over [Formula: see text]. Further, we extend and obtain cyclic codes, [Formula: see text]-constacyclic codes and permutation equivalent to quasi-cyclic codes over [Formula: see text], respectively, as Gray images of skew [Formula: see text]-constacyclic codes over [Formula: see text].

On the linear codes over the ring Rp

2016 ◽  
Vol 08 (02) ◽  
pp. 1650036 ◽  
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis ◽  
Senol Eren
Keyword(s):  
Prime Number ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Constacyclic Codes ◽  
Nontrivial Automorphism ◽  
Macwilliams Identities ◽  
Skew Cyclic Codes ◽  
Quantum Error ◽  
Quasi Cyclic Codes

Some results are generalized on linear codes over [Formula: see text] in [15] to the ring [Formula: see text], where [Formula: see text] is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over [Formula: see text] are obtained. The parameters of quantum error correcting codes are obtained from negacyclic codes over [Formula: see text]. A nontrivial automorphism [Formula: see text] on the ring [Formula: see text] is determined. By using this, the skew cyclic, skew quasi-cyclic, skew constacyclic codes over [Formula: see text] are introduced. The number of distinct skew cyclic codes over [Formula: see text] is given. The Gray images of skew codes over [Formula: see text] are obtained. The quasi-constacyclic and skew quasi-constacyclic codes over [Formula: see text] are introduced. MacWilliams identities of linear codes over [Formula: see text] are given.

Quasi-cyclic codes over the ring 𝔽p[u]/〈u2 − u〉

2015 ◽  
Vol 08 (04) ◽  
pp. 1550085
Author(s):  
Sukhamoy Pattanayak ◽  
Abhay Kumar Singh
Keyword(s):  
Structural Properties ◽  
Cyclic Codes ◽  
Natural Generalization ◽  
Spanning Set ◽  
The One ◽  
Quasi Cyclic Codes

Quasi-cyclic (QC) codes are a natural generalization of cyclic codes. In this paper, we study some structural properties of QC codes over [Formula: see text], where [Formula: see text] is a prime and [Formula: see text]. By exploring their structure, we determine the one generator QC codes over [Formula: see text] and the size by giving a minimal spanning set. We discuss some examples of QC codes of various length over [Formula: see text].

scholarly journals Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

2020 ◽  
Vol 70 (6) ◽  
pp. 626-632
Author(s):  
Om Prakash ◽  
Shikha Yadav ◽  
Ram Krishna Verma
Keyword(s):  
Cyclic Codes ◽  
Gray Map ◽  
Constacyclic Codes ◽  
Dual Codes ◽  
Gray Image ◽  
New Class ◽  
Sharing Scheme ◽  
Lcd Codes ◽  
Reversible Cyclic Codes

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

scholarly journals Efficient Encryption From Random Quasi-Cyclic Codes

2018 ◽  
Vol 64 (5) ◽  
pp. 3927-3943 ◽  
Author(s):  
Carlos Aguilar-Melchor ◽  
Olivier Blazy ◽  
Jean-Christophe Deneuville ◽  
Philippe Gaborit ◽  
Gilles Zemor
Keyword(s):  
Cyclic Codes ◽  
Quasi Cyclic Codes
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