An Extension of the Order Bound for AG Codes

Duursma, Iwan; Kirov, Radoslav

doi:10.1007/978-3-642-02181-7_2

Cited by 9 publications

(9 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is essential in order to attain the actual minimum distance of Hermitian two-point codes and in general greatly improves the order bound. The improved bounds d ABZ ′ , d DP [7] and d DK [6]…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Distance bounds for algebraic geometric codes

Duursma

Kirov

Park

2011

Journal of Pure and Applied Algebra

Self Cite

View full text Add to dashboard Cite

a b s t r a c tVarious methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories, and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Güneri, Stichtenoth, and Taskin, and by Duursma and Park, and of the order bound by Duursma and Park, and by Duursma and Kirov. In this paper, we provide short proofs for all floor bounds and most order bounds in the setting of the van Lint and Wilson AB method. Moreover, we formulate unifying theorems for order bounds and formulate the DP and DK order bounds as natural but different generalizations of the Feng-Rao bound for one-point codes.

show abstract

Section: Introductionmentioning

confidence: 98%

“…C Ω (D, G = 28P + 2Q) C Ω (D, G = 30P + 2Q) 9 9 9 10 10 10 The best bounds overall are the order bounds d DP [7] and d DK [6]. In the second part of the paper we present a framework to derive bounds of order type including the bounds d DP and d DK .…”

Section: Introductionmentioning

confidence: 99%

Distance bounds for algebraic geometric codes

Duursma

Kirov

Park

2011

Journal of Pure and Applied Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…6] the equality between [27,28] and half the bound in [1]. This demonstrates that Andersen and Geil's bound [1] is much more convenient than [2,7,8] in some cases, though the former [1] is implied by the latter [2,7,8].…”

Section: Introductionmentioning

confidence: 96%

“…Finally, a result in a different direction was established in [21] where it was shown that for one-point algebraic geometric codes one can view Andersen and Geil's bound as a consequence of the Beelen bound [2] for more point codes and thereby also as a consequence of the Duursma-Kirov-Park bound [7,8] for such codes. However, it seems prohibitively difficult to prove the equality between the error correction capability of [27,28] and half the bounds in [2,7,8], while we proved in just a few lines [19,Prop. 6] the equality between [27,28] and half the bound in [1].…”

Section: Introductionmentioning

confidence: 99%

Feng–Rao decoding of primary codes

Geil

Matsumoto

Ruano

2013

Finite Fields and Their Applications

View full text Add to dashboard Cite

We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [1] for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Among those are important families of multivariate polynomial codes. Matsumoto and Miura in [30] (See also [3]) derived from the Feng-Rao bound a bound for primary one-point algebraic geometric codes and showed how to decode up to what is guaranteed by their bound. The exposition in [30] requires the use of differentials which was not needed in [1]. Nevertheless we demonstrate a very strong connection between Matsumoto and Miura's bound and Andersen and Geil's bound when applied to primary one-point algebraic geometric codes.

show abstract

“…Esta cota mejora la cota de 56,54,52,51,48,46,44,43,42,41,40,39,38,36,35,34,33,32,31,30,29,28,28,26,25,24,23,22,21,20,21,18,19,16,17,16,13,12,14,10,13,8,12,10,9,8,8,6,8,7,4,5,…”

Section: Semigrupos Numéricosmentioning

confidence: 99%

Pesos de Hamming de códigos Castillo

León¹

View full text Add to dashboard Cite

An Extension of the Order Bound for AG Codes

Cited by 9 publications

References 19 publications

Distance bounds for algebraic geometric codes

Distance bounds for algebraic geometric codes

Feng–Rao decoding of primary codes

Pesos de Hamming de códigos Castillo

Contact Info

Product

Resources

About