English

Linear codes with few weights over $\mathbb{F}_2+u\mathbb{F}_2$

Information Theory 2018-02-28 v1 math.IT

Abstract

In this paper, we construct an infinite family of five-weight codes from trace codes over the ring R=F2+uF2R=\mathbb{F}_2+u\mathbb{F}_2, where u2=0.u^2=0. The trace codes have the algebraic structure of abelian codes. Their Lee weight is computed by using character sums. Combined with Pless power moments and Newton's Identities, the weight distribution of the Gray image of trace codes was present. Their support structure is determined. An application to secret sharing schemes is given.

Keywords

Cite

@article{arxiv.1802.09919,
  title  = {Linear codes with few weights over $\mathbb{F}_2+u\mathbb{F}_2$},
  author = {Minjia Shi and Liqin Qian and Patrick Sole},
  journal= {arXiv preprint arXiv:1802.09919},
  year   = {2018}
}

Comments

14 pages, need help in page 12. arXiv admin note: text overlap with arXiv:1612.00966

R2 v1 2026-06-23T00:35:12.656Z