Title :
Orphans of the first order Reed-Muller codes
Author :
Brualdi, Richard A. ; Pless, Vera S.
Author_Institution :
Dept. of Math., Wisconsin Univ., Madison, WI, USA
fDate :
3/1/1990 12:00:00 AM
Abstract :
If C is a code, an orphan is a coset that is not a descendant. Orphans arise naturally in the investigation of the covering radius. Case C has only even-weight vectors and minimum distance of at least four. Cosets that are orphans are characterized, and then the existence is proved of a family of orphans of first-order Reed-Muller codes R(1, m). For m⩽5 all orphans of R(1, m) are identified
Keywords :
error correction codes; Reed-Muller codes; binary linear codes; coset; covering radius; even-weight vectors; first order codes; minimum distance; orphan; Distributed computing; Linear code; Mathematics; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
