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,...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | text |
| منشور في: |
Animo Repository
2009
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | https://animorepository.dlsu.edu.ph/faculty_research/2775 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| الملخص: | 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. |
|---|