9 research outputs found
A Note on Linear Complementary Pairs of Group Codes
We give a short and elementary proof of the fact that for a linear
complementary pair , where and are -sided ideals in a group
algebra, is uniquely determined by and the dual code is
permutation equivalent to . This includes earlier results of Carlet et al.
and G\"uneri et al. on nD cyclic codes which have been proved by subtle and
lengthy calculations in the space of polynomials.Comment: 5 page
Linear Complementary Pair Of Group Codes over Finite Chain Rings
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of
codes over finite fields have been intensively studied recently due to their
applications in cryptography, in the context of side-channel and fault
injection attacks. The security parameter for an LCP of codes is
defined as the minimum of the minimum distances and . It has
been recently shown that if and are both 2-sided group codes over a
finite field, then and are permutation equivalent. Hence the
security parameter for an LCP of 2-sided group codes is simply .
We extend this result to 2-sided group codes over finite chain rings
On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes
We study one generator quasi-cyclic codes and four-circulant codes, which are
also quasi-cyclic but have two generators. We state the hull dimensions for
both classes of codes in terms of the polynomials in their generating elements.
We prove results such as the hull dimension of a four-circulant code is even
and one-dimensional hull for double-circulant codes, which are special one
generator codes, is not possible when the alphabet size is congruent to 3
mod 4. We also characterize linear complementary pairs among both classes of
codes. Computational results on the code families in consideration are provided
as well.Comment: 16 pages, 8 table
On Linear Complementary Pairs of Codes
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
On linear complementary pairs of codes
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 D are complementary and constacyclic, the codes C and Dâ„ are equivalent to each other. Hence, the security parameter min(d(C), d(Dâ„)) 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 bound is obtained for binary LCP of codes
and a table of values from this bound is presented in the case d(C) = d(Dâ„). This extends the linear programming bound for LCD codes