Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering
Let Fq denote the finite field GF (q) and let b be a positive integer. MDS codes over the symbol alphabet Fqb are considered that are linear over Fq and have sparse ("low-density") parity-check and generator matrices over Fq that are systematic over Fqb. Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an Fq-linear MDS code over Fqb, along with upper bounds on the length of any MDS code that attains those lower bounds. A construction is presented that achieves those bounds for certain redundancy values. The building block of the construction is a set of sparse nonsingular matrices over Fq whose pairwise differences are also nonsingular. Bounds and constructions are presented also for the case where the systematic condition on the parity-check and generator matrices is relaxed to be over Fq, rather than over Fqb. © 1999 IEEE.
Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering
Chi-Leung Wong, Zehra Sura, et al.
I-SPAN 2002
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
Inbal Ronen, Elad Shahar, et al.
SIGIR 2009