Title :
An elementary construction of codes from the groups of units of residue rings of polynomials
Author :
Reid, Les ; Wickham, Cameron
Author_Institution :
Math. Dept., Southwest Missouri State Univ., Springfield, MO, USA
Abstract :
In this note, we present an elementary verification of the minimum distance of some codes constructed by Xing (2002). We show that the codes obtained from this construction are subsets of cosets of linear codes with a given parity-check matrix.
Keywords :
linear codes; parity check codes; polynomials; elementary code construction; linear code; minimum distance; parity-check matrix; polynomial; residue ring; Character generation; Galois fields; Induction generators; Linear code; Mathematics; Parity check codes; Polynomials;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.839540
