Constructed By A Special Matrix Code

A code C can be constructed from a Paley matrix of order n,where n is a power of odd prime. The code contains codewords 0 = (0,0, ...... ,0),1 = (1, 1,..... , 1) and the rows of (S + / + J)/2 and (-5 + / -+- J)/2, where I and J are respectively identity matrix and the matrix with all entries equal to one. In this paper we show the C is an (n, 2(n + 1), (n ?l)/2) code when n = I(mod4); and C is an (n, 2(n + 1), (n - 3)/2) code when n = 3(mod4).Because Conference matrices and Hadamard matrices are related to Paley matrices,in this paper we define the normalized Conference matrices and generalized normalized Hadamard matrices,and we show some special properties of them. Also we constructed a doubly even self-orthogonal code from normalized Conference matrix and a doubly even self-dual code from generalized normalized Hadamard matrix.