Quasi-cyclic codes over Z/sub 4/ and some new binary codes

2002 ◽  
Vol 48 (7) ◽  
pp. 2065-2069 ◽  
Author(s):  
N. Aydin ◽  
D.K. Ray-Chaudhuri
Keyword(s):  
Cyclic Codes ◽  
Binary Codes ◽  
Quasi Cyclic Codes

scholarly journals The homogeneous weight for Rk, related gray map and new binary quasi-cyclic codes

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 885-897 ◽  
Author(s):  
Bahattin Yildiz ◽  
Ismail Kelebek
Keyword(s):  
Coding Theory ◽  
Cyclic Codes ◽  
Gray Map ◽  
Binary Codes ◽  
Binary Images ◽  
Frobenius Rings ◽  
Homogeneous Weights ◽  
Homogeneous Weight ◽  
Theoretical Results ◽  
Quasi Cyclic Codes

Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family Rk, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We find an associated Gray map for the homogeneous weight using first order Reed-Muller codes and we describe some of the general properties of the images of codes over Rk under this Gray map. We then discuss quasi-twisted codes over Rk and their binary images under the homogeneous Gray map. In this way, we find many optimal binary codes which are self-orthogonal and quasi-cyclic. In particular, we find a substantial number of optimal binary codes that are quasi-cyclic of index 8, 16 and 24, nearly all of which are new additions to the database of quasi-cyclic codes kept by Chen.

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.

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 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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