Decoding of linear codes over Galois rings

Babu, N. Suresh; Zimmermann, Karl-Heinz

doi:10.1109/18.923743

Cited by 22 publications

(27 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Let C be a linear code defined on R having a generator matrix in a standard form as in (1). The linear C code is MDR if only if the type of the last nonzero entry in the row is the same or less than the type of its row in the generator matrix which is in standard form.…”

Section: Generator Matrix Of Codes and The Rt Metricmentioning

confidence: 99%

“…Let C be a linear code over R having a generator matrix G in standard form as in (1). If the type of an entry g im i in (1) is of type less than or equal to the types of other entries of the same row, then the minimum RT distance of C is equal to m k .…”

Section: Generator Matrix Of Codes and The Rt Metricmentioning

confidence: 99%

“…. , k s−1 ) -type and length n. Let G be its generator matrix which is in a standard form (1). Furthermore, define π i = q s−j if the row i of the G generator matrix is of type j.…”

Section: Generator Matrix Of Codes and The Rt Metricmentioning

confidence: 99%

See 2 more Smart Citations

Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom–Tsfasman Metric

Özen

Şiap

2006

Des Codes Crypt

View full text Add to dashboard Cite

We investigate the structure of codes over F q [u]/(u s ) rings with respect to the Rosenbloom-Tsfasman (RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We define MDR (maximum distance rank) codes with respect to this metric and give the weights of the codewords of an MDR code. We explore the structure of cyclic codes over F q [u]/(u s ) and show that all cyclic codes over F q [u]/(u s ) rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.

show abstract

Section: Generator Matrix Of Codes and The Rt Metricmentioning

confidence: 99%

Section: Generator Matrix Of Codes and The Rt Metricmentioning

confidence: 99%

See 1 more Smart Citation

Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom–Tsfasman Metric

Özen

Şiap

2006

Des Codes Crypt

View full text Add to dashboard Cite

show abstract

“…Our approach for a lifting decoding scheme has first been studied in [11], then in [5], [7] RS codes over a commutative finite ring have been studied by M. Armand in [1]- [4]. The decoding of interleaved has been studied in [6], [8].…”

Section: B Related Workmentioning

confidence: 99%

A lifting decoding scheme and its application to interleaved linear codes

Quintin

2012

2012 IEEE International Symposium on Information Theory Proceedings

View full text Add to dashboard Cite

Abstract-In this paper we design a decoding algorithm based on a lifting decoding scheme. This leads to a unique decoding algorithm for Reed-Solomon codes over Galois rings with a very low complexity, and a list decoding algorithm. We show that, using erasures in our algorithms, allows to decode more errors than half the minimum distance with a high probability. Finally we apply these techniques to interleaved linear codes over a finite field and obtain a decoding algorithm that can recover more errors than half the minimum distance.

show abstract

“…Vale ressaltar que códigos q-ários são exemplos de códigos cíclicos sobre anéis de cadeia. Em [2], Babu e Zimmermann exibem um algorítimo para decodificação de códigos sobre anéis de Galois, que também são exemplos de anéis de cadeia.…”

unclassified

Códigos cíclicos sobre anéis de cadeia

Silva¹

View full text Add to dashboard Cite

Decoding of linear codes over Galois rings

Cited by 22 publications

References 14 publications

Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom–Tsfasman Metric

Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom–Tsfasman Metric

A lifting decoding scheme and its application to interleaved linear codes

Códigos cíclicos sobre anéis de cadeia

Contact Info

Product

Resources

About