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- W3136133570 abstract "AbstractWe study the k-error linear complexities of de Bruijn sequences. Let n be a positive integer and k be an integer less than (lceil frac{2^{n-1}}{n}rceil ). We show that the k-error linear complexity of a de Bruijn sequence of order n is greater than or equal to (2^{n-1}+1), which implies that de Bruijn sequences have good randomness property with respect to the k-error linear complexity. We also study the compactness of some related bounds, and prove that in the case that (nge 4) and n is a power of 2, there always exists a de Bruijn of order n such that the Hamming weight of (L(mathbf {s})oplus R(mathbf {s})) is (frac{2^{n-1}}{n}), where (L(mathbf {s})) and (R(mathbf {s})) denote respectively the left half and right half of one period of this de Bruijn sequence. Besides, some experimental results are provided for the case that n is not a power of 2.Keywordsk-Error linear complexityde Bruijn sequenceNonlinear feedback shift register" @default.
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- W3136133570 date "2021-01-01" @default.
- W3136133570 modified "2023-09-23" @default.
- W3136133570 title "On the k-Error Linear Complexities of De Bruijn Sequences" @default.
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- W3136133570 doi "https://doi.org/10.1007/978-3-030-71852-7_23" @default.
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