### Abstract

This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.

Original language | English |
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Title of host publication | Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 8th International Conference, AAECC-8, Proceedings |

Publisher | Springer Verlag |

Pages | 96-105 |

Number of pages | 10 |

ISBN (Print) | 9783540541950 |

DOIs | |

Publication status | Published - Jan 1 1991 |

Event | 8th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1990 - Tokyo, Japan Duration: Aug 20 1990 → Aug 24 1990 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 508 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1990 |
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Country | Japan |

City | Tokyo |

Period | 8/20/90 → 8/24/90 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

_{q}-ARY m-sequences. In

*Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 8th International Conference, AAECC-8, Proceedings*(pp. 96-105). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 508 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-54195-0_42

**Substitution of characters in _{q}-ARY m-sequences.** / Vajda, I.; Nemetz, Tibor.

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

_{q}-ARY m-sequences. in

*Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 8th International Conference, AAECC-8, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 508 LNCS, Springer Verlag, pp. 96-105, 8th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1990, Tokyo, Japan, 8/20/90. https://doi.org/10.1007/3-540-54195-0_42

_{q}-ARY m-sequences. In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 8th International Conference, AAECC-8, Proceedings. Springer Verlag. 1991. p. 96-105. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-54195-0_42

}

TY - GEN

T1 - Substitution of characters in q-ARY m-sequences

AU - Vajda, I.

AU - Nemetz, Tibor

PY - 1991/1/1

Y1 - 1991/1/1

N2 - This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.

AB - This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.

UR - http://www.scopus.com/inward/record.url?scp=84935495676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84935495676&partnerID=8YFLogxK

U2 - 10.1007/3-540-54195-0_42

DO - 10.1007/3-540-54195-0_42

M3 - Conference contribution

AN - SCOPUS:84935495676

SN - 9783540541950

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 96

EP - 105

BT - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 8th International Conference, AAECC-8, Proceedings

PB - Springer Verlag

ER -