Pisano period codes
Information Theory
2017-09-15 v1 math.IT
Abstract
The cyclic codes with parity check polynomial the reciprocal of the characteristic polynomial of the Fibonacci recurrence over a prime finite field are shown to have either one weight or two weights. When these codes are irreducible cyclic we obtain many counterexamples to the conjectural classification of two-weight irreducible cyclic codes of Schmidt and White (2002). When they are reducible and projective their duals are uniformly packed.
Cite
@article{arxiv.1709.04582,
title = {Pisano period codes},
author = {Minjia Shi and Zhongyi Zhang and Patrick Sole},
journal= {arXiv preprint arXiv:1709.04582},
year = {2017}
}
Comments
10 pages, submitted on 9th, September