Zeta polynomials of type IV codes over rings of order four
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,...
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oai:animorepository.dlsu.edu.ph:faculty_research-37742021-11-03T06:21:25Z Zeta polynomials of type IV codes over rings of order four Nocon, Ederlina G. 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. 2009-10-30T07:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/2775 Faculty Research Work Animo Repository Rings (Algebra) Finite fields (Algebra) Riemann hypothesis Mathematics |
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Rings (Algebra) Finite fields (Algebra) Riemann hypothesis Mathematics |
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Rings (Algebra) Finite fields (Algebra) Riemann hypothesis Mathematics Nocon, Ederlina G. Zeta polynomials of type IV codes over rings of order four |
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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. |
| format |
text |
| author |
Nocon, Ederlina G. |
| author_facet |
Nocon, Ederlina G. |
| author_sort |
Nocon, Ederlina G. |
| title |
Zeta polynomials of type IV codes over rings of order four |
| title_short |
Zeta polynomials of type IV codes over rings of order four |
| title_full |
Zeta polynomials of type IV codes over rings of order four |
| title_fullStr |
Zeta polynomials of type IV codes over rings of order four |
| title_full_unstemmed |
Zeta polynomials of type IV codes over rings of order four |
| title_sort |
zeta polynomials of type iv codes over rings of order four |
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Animo Repository |
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2009 |
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https://animorepository.dlsu.edu.ph/faculty_research/2775 |
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