Error Patterns

C. Hoede, Z. Li

Research output: Book/ReportReportOther research output

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Abstract

In coding theory the problem of decoding focuses on error vectors. In the simplest situation code words are $(0,1)$-vectors, as are the received messages and the error vectors. Comparison of a received word with the code words yields a set of error vectors. In deciding on the original code word, usually the one for which the error vector has minimum Hamming weight is chosen. In this note some remarks are made on the problem of the elements 1 in the error vector, that may enable unique decoding, in case two or more code words have the same Hamming distance to the received message word, thus turning error detection into error correction. The essentially new aspect is that code words, message words and error vectors are put in one-one correspondence with graphs.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages16
Publication statusPublished - 2001

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1588
ISSN (Print)0169-2690

Fingerprint

Error detection
Decoding
Hamming distance
Error correction

Keywords

  • MSC-94BXX
  • IR-65775
  • EWI-3408

Cite this

Hoede, C., & Li, Z. (2001). Error Patterns. (Memorandum; No. 1588). Enschede: University of Twente, Department of Applied Mathematics.
Hoede, C. ; Li, Z. / Error Patterns. Enschede : University of Twente, Department of Applied Mathematics, 2001. 16 p. (Memorandum; 1588).
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Hoede, C & Li, Z 2001, Error Patterns. Memorandum, no. 1588, University of Twente, Department of Applied Mathematics, Enschede.

Error Patterns. / Hoede, C.; Li, Z.

Enschede : University of Twente, Department of Applied Mathematics, 2001. 16 p. (Memorandum; No. 1588).

Research output: Book/ReportReportOther research output

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T1 - Error Patterns

AU - Hoede, C.

AU - Li, Z.

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PY - 2001

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N2 - In coding theory the problem of decoding focuses on error vectors. In the simplest situation code words are $(0,1)$-vectors, as are the received messages and the error vectors. Comparison of a received word with the code words yields a set of error vectors. In deciding on the original code word, usually the one for which the error vector has minimum Hamming weight is chosen. In this note some remarks are made on the problem of the elements 1 in the error vector, that may enable unique decoding, in case two or more code words have the same Hamming distance to the received message word, thus turning error detection into error correction. The essentially new aspect is that code words, message words and error vectors are put in one-one correspondence with graphs.

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KW - IR-65775

KW - EWI-3408

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Hoede C, Li Z. Error Patterns. Enschede: University of Twente, Department of Applied Mathematics, 2001. 16 p. (Memorandum; 1588).