Handbook of Coding Theory
Graph Theory With Applications
Graph Theory With Applications
LDGM codes for channel coding and joint source-channel coding of correlated sources
EURASIP Journal on Applied Signal Processing
Iterative decoding of binary block and convolutional codes
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
On the covering radius of binary codes (Corresp.)
IEEE Transactions on Information Theory
A recursive approach to low complexity codes
IEEE Transactions on Information Theory
The covering radius of cyclic codes of length up to 31 (Corresp.)
IEEE Transactions on Information Theory
On the covering radius of codes
IEEE Transactions on Information Theory
Covering radius---Survey and recent results
IEEE Transactions on Information Theory
An algorithm for counting short cycles in bipartite graphs
IEEE Transactions on Information Theory
| Hi-index | 0.04 |
Let H"m be the binary linear block code with parity-check matrix H"m whose columns are all distinct binary strings of length m and Hamming weight 2. It is shown that H"m is an [n,k,d]=[m(m-1)2,(m-1)(m-2)2,3] code while the dual-code H"m^@? has dimension k^@? and minimum distance d^@? satisfying k^@?=d^@?=m-1. It is in general very difficult to find or even estimate the covering radius of a given code. It is shown here that the covering radius of H"m, denoted Cr(H"m), is @?m2@?. We also show that Cr(H"m^@?)=m(m-2)4 if m is even and Cr(H"m^@?)=(m-1)^24 if m is odd. Thus Cr(H"m^@?)~Cr(H"m)^2. The weight distribution of H"m^@? is given. This together with the MacWilliams identities results in an expression for the weight distribution of H"m. It turns out that the covering radius of H"m is equal to its external distance. From the Tanner graph perspective, the Tanner graphs of H"m and H"m^@? have girth 6. It is shown that the Tanner graphs of H"m"+"1^@? and H"m are essentially identical and are structurally representable by the complete graph K"m on m vertices.