Generalized Hermitian Codes over GF(2^r)

In: IEEE Transactions on Information Theory. 2006

Authors

• Stanislav Bulygin

Abstract

"In this paper a generalization of Hermitian function field proposed
by A.Garcia and H.Stichtenoth is studied. A Weierstrass semigroup of the
point at infinity for the case $q=2, r\ge 3$ is calculated. It turns out that
unlike Hermitian case, there are already three generators for the semigroup.
This result then is applied to codes, constructed on generalized Hermitian
function fields. Further, results of C.Kirfel and R.Pellikaan are applied to
estimating a Feng-Rao designed distance for GH-codes, which improve on the
Goppa designed minimum distance. Next, the question of codes dual to GH-codes
is studied. It is shown that the duals are also GH-codes and an explicit
formula is given. In particular, this formula enables one to calculate the
parameters of a dual code. A new record-giving $[32,16,\ge 12]$-code over GF
(8) is presented as one of the examples."

Full Text

• Publication: Bulygin06generalized.pdf

BibTeX

 
@Article{ Bulygin06generalized, 
   title = { Generalized Hermitian Codes over GF(2^r) }, 
   author = { Stanislav Bulygin },    
   journal = { IEEE Transactions on Information Theory },             
   year = 2006, 
} 

---

This publication belongs to the project KryFoVe.