Constructions and bounds on linear error-block codes

LİNG S., Ozbudak F.

DESIGNS CODES AND CRYPTOGRAPHY, vol.45, no.3, pp.297-316, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1007/s10623-007-9119-9
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.297-316
  • Middle East Technical University Affiliated: Yes

Abstract

We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert-Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F-2. We also study the asymptotic of linear error-block codes. We define the real valued function alpha (q,m,a) (delta), which is an analog of the important real valued function alpha (q) (delta) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert-Varshamov and algebraic geometry type lower bounds on alpha (q,m,a) (delta). We compare these lower bounds in graphs.