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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Animo Repository
2009
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/2775 |
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| Institution: | De La Salle University |
| Summary: | 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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