𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New Bounds on the Distance Distribution of Extended Goppa Codes

✍ Scribed by Simon Litsyn; Sarit Zur


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
169 KB
Volume
8
Category
Article
ISSN
1071-5797

No coin nor oath required. For personal study only.

✦ Synopsis


We derive new estimates for the error term in the binomial approximation to the distance distribution of extended Goppa codes. This is an improvement on the earlier bounds by Vladuts and Skorobogatov, and Levy and Litsyn.


πŸ“œ SIMILAR VOLUMES


On the Cyclicity of Goppa Codes, Parity-
✍ Thierry P. Berger πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 231 KB

Classical Goppa codes are a special case of Alternant codes. First we prove that the parity-check subcodes of Goppa codes and the extended Goppa codes are both Alternant codes. Before this paper, all known cyclic Goppa codes were some particular BCH codes. Many families of Goppa codes with a cyclic

Bounds on the Minimum Distance of High D
✍ Xiangyu Song; Jeffrey Dill; Alan R. Lindsey πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 132 KB

This paper derives the upper and lower bounds on the minimum distance of 4-ary circular trellis-coded modulation using a simplex signal constellation. The bounds are shown to be tight and reachable, and the code is shown to achieve simplex distance between parallel paths at each stage of the trellis

Upper Bounds on the Covering Radius of a
✍ S. Litsyn; A. TietΓ€vΓ€inen πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 235 KB

We derive new upper bounds on the covering radius of a binary linear code as a function of its dual distance and dual-distance width . These bounds improve on the Delorme -Sole Β΄ -Stokes bounds , and in a certain interval for binary linear codes they are also better than Tieta Β¨ va Β¨ inen's bound .