# Error patterns II

C. Hoede, Z. Li

Research output: Book/ReportReportOther research output

### 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. This note is a continuation of a first investigation of error patterns. First we consider burstiness and distribution of error vectors without assuming cyclic conditions. Then we define some forms of perfectness of codes and pose the problem of finding semi-perfect codes. The results of a systematic search for small vector lengths are presented. Finally a link is laid between error vectors, graphs and balanced incomplete block designs.
Original language English Enschede University of Twente, Department of Applied Mathematics Published - 2002

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1647 0169-2690

Decoding

• MSC-94BXX
• IR-65833
• EWI-3467

### Cite this

Hoede, C., & Li, Z. (2002). Error patterns II. (Memorandum; No. 1647). Enschede: University of Twente, Department of Applied Mathematics.
Hoede, C. ; Li, Z. / Error patterns II. Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1647).
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author = "C. Hoede and Z. Li",
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Hoede, C & Li, Z 2002, Error patterns II. Memorandum, no. 1647, University of Twente, Department of Applied Mathematics, Enschede.

Error patterns II. / Hoede, C.; Li, Z.

Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; No. 1647).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Error patterns II

AU - Hoede, C.

AU - Li, Z.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

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. This note is a continuation of a first investigation of error patterns. First we consider burstiness and distribution of error vectors without assuming cyclic conditions. Then we define some forms of perfectness of codes and pose the problem of finding semi-perfect codes. The results of a systematic search for small vector lengths are presented. Finally a link is laid between error vectors, graphs and balanced incomplete block designs.

AB - 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. This note is a continuation of a first investigation of error patterns. First we consider burstiness and distribution of error vectors without assuming cyclic conditions. Then we define some forms of perfectness of codes and pose the problem of finding semi-perfect codes. The results of a systematic search for small vector lengths are presented. Finally a link is laid between error vectors, graphs and balanced incomplete block designs.

KW - MSC-94BXX

KW - IR-65833

KW - EWI-3467

M3 - Report

T3 - Memorandum

BT - Error patterns II

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Hoede C, Li Z. Error patterns II. Enschede: University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1647).