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Linear codes with few weights over $\mathbb{F}_2+u\mathbb{F}_2$
- Publication Year :
- 2018
-
Abstract
- In this paper, we construct an infinite family of five-weight codes from trace codes over the ring $R=\mathbb{F}_2+u\mathbb{F}_2$, where $u^2=0.$ 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.<br />Comment: 14 pages, need help in page 12. arXiv admin note: text overlap with arXiv:1612.00966
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1802.09919
- Document Type :
- Working Paper