An extension of the codes introduced by Séguin, allard and Bhargava

SCguin, Allard and Bhargava [ 1,4] have recently introduced a class of codes (hereafter called SAB-codes) providing error protection in byte-oriented information systems. In the case of bytes of 8 bits, these authors have proposed a l-error correcting, 2-error detecting linear code of length 8 x 24 and dimension 7 x 23 with one parity byte which may correct any double error affecting two different information bytes. In this paper, we define SAB-codes over any finite field GF(q) for bytes of any length 1 and applying some theorems in finite geometry [2, 31 we give general constructions which in the binary case and for bytes of length 8 improve the code studied in 141. We also give a decoding algorithm based on the geometric properties of the construction.