On the minimum distance of combinatorial codes

Combinatorial analysis of the minimum distance of turbo codes

In this paper, new upper bounds on the maximum attainable minimum Hamming distance of Turbo codes with arbitrary — including the best — interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, on the code rate and on the scramblers employed in the encoder. Examples of the new bounds for particular Turbo codes are given and discussed. The ...

Lattice polytopes in coding theory

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations. 2010 MSC: 14M25, 14G50,...

Combinatorial Analysis of the Minimum Distance of Turbo Codes

The combinatorics of LCD codes: linear programming bound and orthogonal matrices

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings Rk. We give a linear programming bound on the largest size of an LCD code of given length and minimum distance. We make a table of lower bounds for this combinatoria...

Parameters of Goppa codes revisited

We discuss parameters of Goppa codes, such as minimum distance, covering radius, distance distribution, and generalized Hamming weights. By a variation on the exponential sums method and combinatorial arguments, we sharpen known bounds.