S-Code: new MDS array codes with optimal encoding

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. We also give a description of which slopes other than 1 and -1 can be used to construct S-Codes.