S-code: new distance-3 MDS array codes

In this paper, we present a new description of the X-code, a class of MDS array code, using skews, named S-code. The X-codes result in codewords that are arrays of size n × n, where n is prime. Our new description does not require n to be prime but requires n to be an odd number with smallest prime factor greater than 3. We prove that the S-codes result in a distance-3 MDS code and give a description of which slopes other than 1 and -1 can be used to construct S-codes. Encoding and decoding procedures of the S-code are also introduced.