Constructions and bounds on linear error-block codes

• Main Authors: Ling, San, Özbudak, Ferruh
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Cryptography
• Online Access: https://hdl.handle.net/10356/96410; http://hdl.handle.net/10220/9851
• Institution: Nanyang Technological University

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 . We also study the asymptotic of linear error-block codes. We define the real valued function α q,m,a (δ), which is an analog of the important real valued function α q (δ) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert–Varshamov and algebraic geometry type lower bounds on α q,m,a (δ). We compare these lower bounds in graphs.