English

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.

Keywords

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

R2 v1 2026-06-22T21:42:36.854Z