By Huaxiong Wang, Yongqing Li, Shengyuan Zhang

Li Y., Ling S., Niederreiter H., Wang H., Xing C. (eds.) Coding and Cryptology.. complaints of the overseas Workshop, Wuyi Mountain, Fujian, China, 11-15 June 2007 (WS, 2008)(ISBN 9812832238)(O)(288s)

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**Extra resources for Coding and cryptology: proceedings of the international workshop, Wuyi Mountain, Fujian, China 11-15 June 2007**

**Example text**

A binary string of length 2n , f = [f (0, 0, . . , 0), f (1, 0, . . , 0), f (0, 1, . . , 0), f (1, 1, . . , 0), . . , f (1, 1, . . , 1)]. The Hamming weight wt(f ) of f is the weight of this string, that is, the size of the support supp(f ) = {x ∈ F2n ; f (x) = 1} of the function. , the XOR). We say that a Boolean function f is balanced if its truth table contains an equal number of 1’s and 0’s, that is, if its Hamming weight equals 2n−1 . The truth table does not give an idea of the algebraic complexity of the function.

The polynomials fn− , fn± were constructed and applied to coding theory by Levenshtein [4–6]. Polynomials closely related to them were studied May 23, 2008 13:28 WSPC - Proceedings Trim Size: 9in x 6in series 20 in a more general context in the works of M. G. ; see Krein and ± Nudelman [8]. The orthogonal systems {p− i }, {pi } are sometimes called adjacent polynomials of the original system {pi }. 2. The stationary points found above are not true extremums because the second differential of the functionals F, F (−) , F(±) is undefined: for instance, d2 F(g) = 2 (x − s)h, h .

Braeken, J. Lano, N. Mentens, B. Preneel and I. Verbauwhede. SFINKS: A Synchronous stream cipher for restricted hardware environments. SKEW Symmetric Key Encryption Workshop, 2005. 7. A. Braeken, J. Lano and B. Preneel. Evaluating the Resistance of Filters and Combiners Against Fast Algebraic Attacks. Eprint on ECRYPT, 2005. 8. A. Braeken and B. Preneel. On the Algebraic Immunity of Symmetric Boolean Functions. In Indocrypt 2005, number 3797 in LNCS, pp. 35–48. Springer Verlag, 2005. org/, May 23, 2008 13:28 WSPC - Proceedings Trim Size: 9in x 6in series 42 No.