Quasi-Cyclic Codes from a Finite Affine Plane

Authors:
Norifumi Kamiya;Marc P. Fossorier
Affiliations:
Internet Systems Research Laboratories, NEC Corporation, Nakahara, Kawasaki, Japan 211-8666;Department of Electrical Engineering, University of Hawaii at Manoa, Honolulu, USA 96822
Venue:
Designs, Codes and Cryptography
Year:
2006

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Abstract

Finite geometry codes are defined as the null spaces of the incidence matrices of points and flats in finite geometries. In this paper, we investigate the incidence matrix of points other than the origin and lines not passing through the origin in the affine plane AG(2,2s), and we present two classes of quasi-cyclic codes derived from submatrices of the point-line incidence matrix. We also investigate the 2-ranks of those submatrices.