Cross-Joins in de Bruijn Sequences and Maximum Length Linear Sequences

Taejoo CHANG; Iickho SONG; Hyung Myung KIM; Sung Ho CHO

Cross-Joins in de Bruijn Sequences and Maximum Length Linear Sequences

Taejoo CHANG, Iickho SONG, Hyung Myung KIM, Sung Ho CHO

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In this paper, a construction of de Bruijn sequences using maximum length linear sequences is considered. The construction is based on the well-known cross-join (CJ) method: Maximum length linear sequences are used to produce de Bruijn sequences by the CJ process. Properties of the CJ paris in the maximum length linear sequences are investigated. It is conjectured that the number of CJ pairs in a maximum length linear sequence is given by (2^2n-3+1)/3-2^n-2, where n2 is the length of the linear feedback shift register with the sequence. The CJ paris for some special cases are obtained. An algorithm for finding CJ pairs is described and a method of implementation is discussed briefly.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.9 pp.1494-1501

Publication Date: 1993/09/25

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Type of Manuscript: PAPER

Category: Information Theory and Coding Theory

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Taejoo CHANG, Iickho SONG, Hyung Myung KIM, Sung Ho CHO, "Cross-Joins in de Bruijn Sequences and Maximum Length Linear Sequences" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 9, pp. 1494-1501, September 1993, doi: .
Abstract: In this paper, a construction of de Bruijn sequences using maximum length linear sequences is considered. The construction is based on the well-known cross-join (CJ) method: Maximum length linear sequences are used to produce de Bruijn sequences by the CJ process. Properties of the CJ paris in the maximum length linear sequences are investigated. It is conjectured that the number of CJ pairs in a maximum length linear sequence is given by (2^2n-3+1)/3-2^n-2, where n2 is the length of the linear feedback shift register with the sequence. The CJ paris for some special cases are obtained. An algorithm for finding CJ pairs is described and a method of implementation is discussed briefly.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_9_1494/_p

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@ARTICLE{e76-a_9_1494,
author={Taejoo CHANG, Iickho SONG, Hyung Myung KIM, Sung Ho CHO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cross-Joins in de Bruijn Sequences and Maximum Length Linear Sequences},
year={1993},
volume={E76-A},
number={9},
pages={1494-1501},
abstract={In this paper, a construction of de Bruijn sequences using maximum length linear sequences is considered. The construction is based on the well-known cross-join (CJ) method: Maximum length linear sequences are used to produce de Bruijn sequences by the CJ process. Properties of the CJ paris in the maximum length linear sequences are investigated. It is conjectured that the number of CJ pairs in a maximum length linear sequence is given by (2^2n-3+1)/3-2^n-2, where n2 is the length of the linear feedback shift register with the sequence. The CJ paris for some special cases are obtained. An algorithm for finding CJ pairs is described and a method of implementation is discussed briefly.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Cross-Joins in de Bruijn Sequences and Maximum Length Linear Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1494
EP - 1501
AU - Taejoo CHANG
AU - Iickho SONG
AU - Hyung Myung KIM
AU - Sung Ho CHO
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1993
AB - In this paper, a construction of de Bruijn sequences using maximum length linear sequences is considered. The construction is based on the well-known cross-join (CJ) method: Maximum length linear sequences are used to produce de Bruijn sequences by the CJ process. Properties of the CJ paris in the maximum length linear sequences are investigated. It is conjectured that the number of CJ pairs in a maximum length linear sequence is given by (2^2n-3+1)/3-2^n-2, where n2 is the length of the linear feedback shift register with the sequence. The CJ paris for some special cases are obtained. An algorithm for finding CJ pairs is described and a method of implementation is discussed briefly.
ER -