Asymptotically good convolutional codes. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: La Guardia, Giuliano G.
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 7(2019)
• Page Start: 1483
• Page End: 1494
• Publication Date: 2019-07-03
• Subjects: Convolutional codes -- transitive codes -- code construction; 11T71; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1459448
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: In this paper, we construct new sequences of asymptotically good convolutional codes (AGCC's). These sequences are obtained from sequences of transitive, self-orthogonal and self-dual algebraic geometry (AG) codes attaining the Tsfasman–Vladut–Zink bound. Furthermore, by applying the techniques of expanding, extending, puncturing, direct sum, the ⟨ u | u + v ⟩ construction and the product code construction to these block codes, we construct more new sequences of asymptotically good convolutional codes. Additionally, we show that the new constructions presented here also hold when applied to al l sequences of asymptotically good block codes where lim j → ∞ k j / n j and lim j → ∞ d j / n j exist.