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How Many Bits have to be Changed to Decrease the Linear Complexity?

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Abstract

The k-error linear complexity of periodic binary sequences is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. For the period length p n, where p is an odd prime and 2 is a primitive root modulo p 2, we show a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. Moreover, we describe an algorithm to determine the k-error linear complexity of a given p n-periodic binary sequence.

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Authors
  1. Wilfried Meidl
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Meidl, W. How Many Bits have to be Changed to Decrease the Linear Complexity?. Designs, Codes and Cryptography 33, 109–122 (2004). https://doi.org/10.1023/B:DESI.0000035466.28660.e9

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  • DOI: https://doi.org/10.1023/B:DESI.0000035466.28660.e9

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