On the Minimum Linear Complexity of de Bruijn Sequences over Non-prime Finite Fields

Hines, Peter A.

doi:10.1006/jcta.1998.2920

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Cited by 3 publications

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Linear complexity of sequences

Etzion

2024

Sequences and the De Bruijn Graph

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Linear complexity of sequences

Etzion

2024

Sequences and the De Bruijn Graph

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Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/

Lauder

Paterson

2003

IEEE Trans. Inform. Theory

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Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We p r e s e n t an algorithm which computes the error linear complexity for binary sequences of period`= 2 n using O(`(log`) 2) bit operations. The algorithm generalises both the Games-Chan and Stamp-Martin algorithms, which compute the linear complexity a n d t h e k-error linear complexity of a binary sequence of period`= 2 n , respectively. We also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of Reed-Muller codes.

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On Duplication-Free Codes for Disjoint or Equal-Length Errors

Yu,

Schwartz

2024

Preprint

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Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors. We construct codes, with positive asymptotic rate, for the two settings, as well as for their combination. Our constructions are duplication-free codes, comprising codewords that do not contain tandem duplications of specific lengths. Additionally, our codes generalize previous constructions, containing them as special cases. MSC Classification: 68R15 , 94B25 , 94B35

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On the Minimum Linear Complexity of de Bruijn Sequences over Non-prime Finite Fields

Abstract: It has been conjectured that over any non-prime finite field F p m and for any positive integer n, there exists a span n de Bruijn sequence over F p m which has the minimum possible linear complexity p nm&1 +n. We give a proof by construction that this conjecture is true. Academic Press

Cited by 3 publications

References 9 publications

Linear complexity of sequences

Linear complexity of sequences

Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/

On Duplication-Free Codes for Disjoint or Equal-Length Errors

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