Reed-Solomon Codes over Fields of Characteristic Zero

Carmen Sippel; Cornelia Ott; Sven Puchinger; Martin Bossert

doi:10.1109/ISIT.2019.8849332

Reed-Solomon Codes over Fields of Characteristic Zero

Carmen Sippel, Cornelia Ott, Sven Puchinger, Martin Bossert

Computation, Information and Technology

University of Ulm

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We study Reed-Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during encoding and the bit complexity of decoding, which is polynomial in the code length and in the bit width of error and codeword values. The results can be generalized to arbitrary number fields.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1537-1541
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849332
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

Access to Document

10.1109/ISIT.2019.8849332

Cite this

Sippel, C., Ott, C., Puchinger, S., & Bossert, M. (2019). Reed-Solomon Codes over Fields of Characteristic Zero. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1537-1541). Article 8849332 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849332

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title = "Reed-Solomon Codes over Fields of Characteristic Zero",

abstract = "We study Reed-Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during encoding and the bit complexity of decoding, which is polynomial in the code length and in the bit width of error and codeword values. The results can be generalized to arbitrary number fields.",

author = "Carmen Sippel and Cornelia Ott and Sven Puchinger and Martin Bossert",

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year = "2019",

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doi = "10.1109/ISIT.2019.8849332",

language = "English",

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Sippel, C, Ott, C, Puchinger, S & Bossert, M 2019, Reed-Solomon Codes over Fields of Characteristic Zero. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849332, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 1537-1541, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849332

Reed-Solomon Codes over Fields of Characteristic Zero. / Sippel, Carmen; Ott, Cornelia; Puchinger, Sven et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1537-1541 8849332 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We study Reed-Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during encoding and the bit complexity of decoding, which is polynomial in the code length and in the bit width of error and codeword values. The results can be generalized to arbitrary number fields.

AB - We study Reed-Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during encoding and the bit complexity of decoding, which is polynomial in the code length and in the bit width of error and codeword values. The results can be generalized to arbitrary number fields.

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Reed-Solomon Codes over Fields of Characteristic Zero

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