On the minimum distance of combinatorial codes

On the minimum distance of combinatorial codes

A conjecture of Da Rocha concerning the minimum distance of a class of combinatorial codes is proven.

Combinatorial Analysis of the Minimum Distance of Turbo 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 ...

A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes. We define syndro...

The Minimum Distance of Graph Codes

We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other geometries. We give results on the minimum distances of the codes.