Simple Estimation for the Dimension of Subfield Subcodes of AG Codes

Tomoharu SHIBUYA
Ryutaroh MATSUMOTO
Kohichi SAKANIWA

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A    No.11    pp.2058-2065
Publication Date: 1997/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
Keyword: 
algebraic geometric code,  dimension of subfield subcode,  class of algebraic curve Cab,  

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Summary: 
In this paper, we present a lower bound for the dimension of subfield subcodes of residue Goppa codes on the curve Cab, which exceeds the lower bound given by Stichtenoth when the number of check symbols is not small. We also give an illustrative example which shows that the proposed bound for the dimension of certain residue Goppa code exceeds the true dimension of a BCH code with the same code length and designed distance.