On the average Hamming distance for binary codes

Trellis-Coded Quantization Based on Maximum-Hamming-Distance Binary Codes

Most design approaches for trellis-coded quantization take advantage of the duality of trellis-coded quantization with trellis-coded modulation, and use the same empiricallyfound convolutional codes to label the trellis branches. This letter presents an alternative approach that instead takes advantage of maximum-Hamming-distance convolutional codes. The proposed source codes are shown to be co...

Lower bounds on the minimum average distance of binary codes

Let β(n,M) denote the minimum average Hamming distance of a binary code of length n and cardinality M. In this paper we consider lower bounds on β(n,M). All the known lower bounds on β(n,M) are useful when M is at least of size about 2n−1/n. We derive new lower bounds which give good estimations when size of M is about n. These bounds are obtained using linear programming approach. In particula...

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

Ternary Hamming and binary perfect covering codes

Given 1 1n € Z, the n-cube Q, is the graph with vertex set V : {0, l}' and ed"geset n:VT:orfi, where f' : {(r,w) e V xV: (u _ w)i:1if and only if j: i,(j:0,.'. ,n-l)), for i:0,... ,n-1. The edges of/t aresaidtohave (ortolie along) the directioni,for i 0,.. . ,n-!.Given a graph G, we say that S gVG) is a perfect dom'inating sei (or PDS) of G if every u € V(G) \ S is neighbor of exactly one verte...

Geometric Construction Codes of Hamming Distance-8

A new high rate binary linear block code construction technique, named as Geometric Construction (GC) codes, was proposed recently [1]. It generates all the even full information rate (optimal) Hamming distance – 4 codes. In this paper, we have enhanced the construction of GC codes with respect to code rate and derived a code family of hamming distance-8 GC codes.