Zeta polynomials of type IV codes over rings of order four

Authors

Ederlina G. Nocon, De La Salle University, Manila

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Kyushu Journal of Mathematics

Volume

63

Issue

2

First Page

209

Last Page

237

Publication Date

10-30-2009

Abstract

We extend the definition of zeta function and zeta polynomial to codes defined over finite rings with respect to a specified weight function. Moreover, we also investigate the Riemann hypothesis analogue for Type IV codes over any of the rings Z4, F2 + uF2 and F2 + vF2. Although, for small lengths, there are only a few actual Type IV codes over Z4, F2 + uF2 or F2 + vF2 that satisfy the Hamming distance upper bound 2(1 + ⌊ n/6 ⌋), we will show that zeta polynomials corresponding to these weight enumerators that meet this bound satisfy the Riemann hypothesis analogue property. © 2009 Faculty of Mathematics, Kyushu University.

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Digitial Object Identifier (DOI)

10.2206/kyushujm.63.209

Recommended Citation

Nocon, E. G. (2009). Zeta polynomials of type IV codes over rings of order four. Kyushu Journal of Mathematics, 63 (2), 209-237. https://doi.org/10.2206/kyushujm.63.209

Disciplines

Mathematics

Keywords

Rings (Algebra); Finite fields (Algebra); Riemann hypothesis

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