Coding and information theory
Linear Codes with Non-Uniform Error Correction Capability
Designs, Codes and Cryptography
Handbook of Coding Theory
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A binary linear code in F"2^n with dimension k and minimum distance d is called an [n,k,d] code. A t-(n,m,@l) design D is a set X of n points together with a collection of m-subsets of X (called a block) such that every t-subset of X is contained in exactly @l blocks. A constant length code which corrects different numbers of errors in different code words is called a non-uniform error correcting code. Parity sectioned reduction of a linear code gives a non-uniform error correcting code. In this paper a new code, [2^n-1,n,2^n^-^1], is developed. The error correcting capability of this code is 2^n^-^2-1=e. It is shown that this code holds a 2-(2^n-1,2^n^-^1,2^n^-^2) design. Also the parity sectioned reduction code after deleting the same g(@?e) positions of each code word of this code holds a 1-(2^n-1-g,2^n^-^1-j,C"jg.2^n^-^1^-^g) design for n=3,g=1,2,...,e and j=0,1,...,g.