On subset subcodes of linear codes

Abstract

We consider a problem of finding codes over alphabets whose size s is not equal to the size of any finite field. We adopted an approach when a linear block code is taken over some finite field GF(q) such that q >; s. Then a subcode is being found such that all the code symbols of all its codewords belong to a subset of GF(q) of size s. Upper and lower bounds on the cardinality of the subset subcode are given. Also coding procedures are considered. Error detection and/or correction procedures are those of the parent code.