MULTIPLE-CYCLIC CODES

Most of the important codes fall in the category of cyclic codes. However the study of cyclic codes is confined to considering overall cyclic shifts of code vectors. Also the study of random-error correction is being made in a setting which is in fact unrealistic, because as the length of the code words increases the number of possible random errors also increases; the number of increased random errors is to be naturally found in the increased part of the word length. Thus practical considerations lead us to think that random errors are suitably phased over the word length.

In this paper the phasing aspects are considered in terms of cyclic blocks so that a code word is composed of several blocks, each block having a cyclic structure. Polynomial representations are developed under a new algebraic setting. A characterization theorem, matrix description, and representation in terms of roots in some known field arc provided.