Z8-Kerdock codes and pseudorandom binary sequences

The Z8 -analogues of the Kerdock codes of length n=2m were introduced by Carlet in 1998. We study the binary sequences of period n - 1 obtained from their cyclic version by using the most significant bit (MSB)-map.The relevant Boolean functions are of degree 4 in general. The linear span of t...

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Main Authors: Lahtonen, Jyrki, Ling, San, Sole, Patrick, Zinoviev, Dmitrii
其他作者: School of Physical and Mathematical Sciences
格式: Article
語言:English
出版: 2013
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在線閱讀:https://hdl.handle.net/10356/98360
http://hdl.handle.net/10220/9844
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機構: Nanyang Technological University
語言: English
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總結:The Z8 -analogues of the Kerdock codes of length n=2m were introduced by Carlet in 1998. We study the binary sequences of period n - 1 obtained from their cyclic version by using the most significant bit (MSB)-map.The relevant Boolean functions are of degree 4 in general. The linear span of these sequences has been known to be of the order of m4. We will show that the crosscorrelation and nontrivial autocorrelation of this family are both upper bounded by a small multiple of v4. The nonlinearity of these sequences has a similar lower bound. A generalization of the above results to the alphabet Z2l, l >= 4 is sketched out.