A Bound on the Minimum Distance of Quasi-cyclic Codes

2012 ◽  
Vol 26 (4) ◽  
pp. 1781-1796 ◽  
Author(s):  
Cem Güneri̇ ◽  
Ferruh Özbudak
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Quasi Cyclic Codes

QUASI-CYCLIC CODES FROM CYCLIC-STRUCTURED DESIGNS WITH GOOD PROPERTIES

2011 ◽  
Vol 03 (02) ◽  
pp. 223-243
Author(s):  
CHRISTOS KOUKOUVINOS ◽  
DIMITRIS E. SIMOS
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Optimization Problem ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Mathematical Structure ◽  
Combinatorial Optimization Problem ◽  
Supersaturated Designs ◽  
Statistical Designs ◽  
Quasi Cyclic Codes

In this paper, one-generator binary quasi-cyclic (QC) codes are explored by statistical tools derived from design of experiments. A connection between a structured cyclic class of statistical designs, k-circulant supersaturated designs and QC codes is given. The mathematical structure of the later codes is explored and a link between complementary dual binary QC codes and E(s2)-optimal k-circulant supersaturated designs is established. Moreover, binary QC codes of rate 1/3, 1/4, 1/5, 1/6 and 1/7 are found by utilizing a genetic algorithm. Our approach is based on a search for good or best codes that attain the current best-known lower bounds on the minimum distance of linear codes, formulated as a combinatorial optimization problem. Surveying previous results, it is shown, that our codes reach the current best-known lower bounds on the minimum distance of linear codes with the same parameters.

scholarly journals q-ary Quasi-Cyclic Codes on Matroid Theory

2018 ◽  
Vol 173 ◽  
pp. 03095
Author(s):  
Li Xiuli ◽  
Zhao Pengcheng ◽  
Zhou Dangsheng
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Matroid Theory ◽  
Generator Matrix ◽  
The Relationship ◽  
Quasi Cyclic Codes

In this paper, rate 1/p q-ary systematic quasi-cyclic codes are constructed based on matroid theory. The relationship between the generator matrix and minimum distance d is derived. Examples and algorithm are presented.

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].

Use of Grobner bases to decode binary cyclic codes up to the true minimum distance

1994 ◽  
Vol 40 (5) ◽  
pp. 1654-1661 ◽  
Author(s):  
Xuemin Chen ◽  
I.S. Reed ◽  
T. Helleseth ◽  
T.K. Truong
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Gröbner Bases ◽  
Grobner Bases
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