On Linear Complementary Pairs of Codes

被引:49
作者
Carlet, Claude [1 ,2 ]
Guneri, Cem [3 ]
Ozbudak, Ferruh [4 ,5 ]
Ozkaya, Buket [3 ,6 ]
Sole, Patrick [7 ]
机构
[1] Univ Paris VIII, Dept Math, F-93526 St Denis, France
[2] Univ Paris XIII, LAGA, CNRS, UMR 7539, F-93526 St Denis, Reunion, France
[3] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey
[4] Middle East Tech Univ, Dept Math, TR-06800 Ankara, Turkey
[5] Middle East Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkey
[6] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore
[7] Univ Paris 08, CNRS, LAGA, F-93526 St Denis, France
关键词
Constacyclic code; quasi-cyclic code; LCP of codes; linear programming bound; QUASI-CYCLIC CODES; ALGEBRAIC STRUCTURE;
D O I
10.1109/TIT.2018.2796125
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We study linear complementary pairs (LCP) of codes (C, D), where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasicyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes. Our result for the constacyclic complementary pairs extends the characterization of linear complementary dual (LCD) cyclic codes given by Yang and Massey. We observe that when C and I) are complementary and constacyclic, the codes C and D-perpendicular to are equivalent to each other. Hence, the security parameter min(d(C), d(D-perpendicular to)) for LCP of codes is simply determined by one of the codes in this case. The same holds for a special class of quasi-cyclic codes, namely 2D cyclic codes, but not in general for all quasi-cyclic codes, since we have examples of LCP of double circulant codes not satisfying this conclusion for the security parameter. We present examples of binary LCP of quasi-cyclic codes and obtain several codes with better parameters than known binary LCD codes. Finally, a linear programming hound is obtained for binary LCP of codes and a table of values from this bound is presented in the case d(C) = d(D-perpendicular to). This extends the linear programming bound for LCD codes.
引用
收藏
页码:6583 / 6589
页数:7
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