Abstract
The well-known Tsfasman-Vladut-Zink (TVZ) theorem states that for all prime powers q = l 2 ≥ 49 there exist sequences of linear codes over \({\mathbb{F}_q}\) with increasing length whose limit parameters R and δ (rate and relative minimum distance) are better than the Gilbert-Varshamov bound. The basic ingredients in the proof of the TVZ theorem are sequences of modular curves (or their corresponding function fields) having many rational points in comparison to their genus (more precisely, these curves attain the so-called Drinfeld-Vladut bound). Starting with such a sequence of curves and using Goppa’s construction of algebraic geometry (AG) codes, one easily obtains sequences of linear codes whose limit parameters beat the Gilbert-Varshamov bound.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
