Tokyo Journal of Mathematics

On Some Properties of the Hyper-Kloosterman Codes

Koji CHINEN

Abstract

The hyper-Kloosterman code was first defined as a trace code by Chinen-Hiramatsu [1]. In this article, two basic parameters of it, the minimum distance and the dimension are estimated. Analysis of the dimension shows that it is one of few examples of trace codes, of which the dimensions do not reduce when taking the trace, and are determined explicitly. It is also shown that the hyper-Kloosterman code can be realized as a quasi-cyclic code. It implies a method of explicit construction of quasi-cyclic codes of a new type.

Article information

Source
Tokyo J. Math., Volume 26, Number 1 (2003), 55-65.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208682

Digital Object Identifier
doi:10.3836/tjm/1244208682

Mathematical Reviews number (MathSciNet)
MR1981999

Zentralblatt MATH identifier
1041.11082

Citation

CHINEN, Koji. On Some Properties of the Hyper-Kloosterman Codes. Tokyo J. Math. 26 (2003), no. 1, 55--65. doi:10.3836/tjm/1244208682. https://projecteuclid.org/euclid.tjm/1244208682

References

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