二元序列的二次复杂度

Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214) Pub Date : 1998-09-07 DOI:10.1109/COMSIG.1998.736944

W. Penzhorn

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引用次数: 1

摘要

在安全通信等应用中，二进制序列的线性复杂性是一个重要的属性。本文引入了二元序列的二次复杂度的概念。结果表明，该复杂度度量与原始Reed-Muller码理论密切相关。利用Reed-Muller码的奇偶校验多项式h(x)，提出了一种计算序列二次复杂度曲线的新算法。实验结果证实了预期的理论和实际行为之间的密切相似。

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Quadratic complexity of binary sequences

The linear complexity of a binary sequences is an important attribute in applications such as secure communications. In this article we introduce the concept of quadratic complexity of a binary sequences. It is shown that this complexity measure is closely linked to the theory of primitive Reed-Muller codes. Making use of the parity-check polynomial h(x) of a Reed-Muller code, a new algorithm for the computation of the quadratic complexity profile of a sequence is developed. Experimental results confirm the close resemblance between expected theoretical and practical behaviour.

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Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214)

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