Name
Abstract | ||
|---|---|---|
An integer-valued function f(x) on the integers that is periodic of period p^e, p prime, can be matched, modulo p^m, by a polynomial function w(x); we show that w(x) may be taken to have degree at most (m(p-1)+1)p^e^-^1-1. Applications include a short proof of the theorem of McEliece on the divisibility of weights of codewords in p-ary cyclic codes by powers of p, an elementary proof of the Ax-Katz theorem on solutions of congruences modulo p, and results on the numbers of codewords in p-ary linear codes with weights in a given congruence class modulo p^e. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.disc.2004.10.030 | Discrete Mathematics |
Keywords | Field | DocType |
11b50,ax-katz,11t71,11t06,weights,coding theory,ax–katz,codes,05a10,polynomials,mceliece,cyclic code,linear code,value function | Prime (order theory),Discrete mathematics,Combinatorics,Polynomial,Multiplicative group of integers modulo n,Modulo,Elementary proof,Root of unity modulo n,Linear code,Mathematics,Primitive root modulo n | Journal |
Volume | Issue | ISSN |
306 | 23 | Discrete Mathematics |
Citations | PageRank | References |
7 | 0.68 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard M. Wilson | 1 | 697 | 340.86 |