On a new code, [2n−1,n,2n−1]

AbstractA binary linear code in F2n with dimension k and minimum distance d is called an [n,k,d] code. A t-(n,m,λ) 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 λ 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, [2n−1,n,2n−1], is developed. The error correcting capability of this code is 2n−2−1=e. It is shown that this code holds a 2-(2n−1,2n−1,2n−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-(2n−1−g,2n−1−j,Cjg.2n−1−g) design for n≥3,g=1,2,…,e and j=0,1,…,g