Constructions and bounds on linear error-block codes
Date of Issue2007
School of Physical and Mathematical Sciences
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.
Designs, codes and cryptography
© 2007 Springer Science+Business Media. This is the author created version of a work that has been peer reviewed and accepted for publication by Designs, Codes and Cryptography, Springer Science+Business Media. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10623-007-9119-9].