Published December 6, 2006
| public
Journal Article
A lemma on polynomials modulo p^m and applications to coding theory
- Creators
- Wilson, Richard M.
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.
Additional Information
© 2006 Elsevier B.V. Received 8 January 2004; revised 22 September 2004; accepted 24 October 2004. Available online 24 July 2006.Additional details
- Eprint ID
- 24480
- DOI
- 10.1016/j.disc.2004.10.030
- Resolver ID
- CaltechAUTHORS:20110720-095319774
- Created
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2011-07-21Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field