Binary codes from Paley graphs of prime-power-square order

Abstract

We examine the binary code from the row span of an adjacency matrix of the Paley graph of order q2, where q is a prime power such that q2≡1(mod8). We show that the code and its dual are respectively [q2,q2−12,q+1]2 and [q2,q2+12,q]2 codes. We obtain spanning sets of minimum-weight vectors for these codes, and in the case of q a prime we show that the code can be used for partial permutation decoding using a certain information set.