By Claude Carlet (auth.), Marc P. C. Fossorier, Hideki Imai, Shu Lin, Alain Poli (eds.)

This publication constitutes the refereed complaints of the sixteenth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16, held in Las Vegas, NV, united states in February 2006.

The 25 revised complete papers offered including 7 invited papers have been conscientiously reviewed and chosen from 32 submissions. one of the topics addressed are block codes; algebra and codes: earrings, fields, and AG codes; cryptography; sequences; interpreting algorithms; and algebra: buildings in algebra, Galois teams, differential algebra, and polynomials.

**Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 16th International Symposium, AAECC-16, Las Vegas, NV, USA, February 20-24, 2006. Proceedings PDF**

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**Additional info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 16th International Symposium, AAECC-16, Las Vegas, NV, USA, February 20-24, 2006. Proceedings**

**Example text**

On Generalized Parity Checks 33 Proof. Let (x0 , x1 , . . , a list of the M = 2k elements of X k such that x0 = 0 and dH (xi , xi+1 ) = 1 for i = 0, 1, . . , M −2. , and f = f0 . , and f = f1 . 2. Let X = {0, 1, 2}. Every (k, 3) GPC is monomially equivalent to f0 (x) = x1 + · · · + xk (mod 3). Alternatively, every (k, 3) GPC is of the form f (x) = a1 x1 + · · · + ak xk + b, where a1 , . . , ak are from GF (3)∗ , and b ∈ GF (3). Proof. We will show that if f (x) ∈ F (k, 3), and f (x) = f0 (x) for all x ∈ B(0), that f (x) = f0 (x) for all x ∈ X k .

In 9th IMA Conference on Cryptography and Coding, 2003. 53. O. S. Rothaus. On “bent” functions, J. Comb. Theory, 20A, 300-305, 1976. 54. E. Pasalic, T. Johansson, S. Maitra and P. Sarkar. New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity. Proceedings of the Workshop on Coding and Cryptography 2001, published by Electronic Notes in Discrete Mathematics, Elsevier, vo. 6, pp. 425-434, 2001. 55. P. Sarkar and S. Maitra. Construction of nonlinear Boolean functions with important cryptographic properties.

Nonlinearity Criteria for Cryptographic Functions, Advances in Cryptology, EUROCRYPT’ 89, Lecture Notes in Computer Science 434, pp. 549-562, Springer Verlag, 1990. 48. W. Meier, E. Pasalic and C. Carlet. Algebraic attacks and decomposition of Boolean functions. Advances in Cryptology, EUROCRYPT 2004, Lecture Notes in Computer Science, Springer Verlag 3027, pp. 474-491, 2004. 28 C. Carlet 49. D. Olej´ ar and M. Stanek. ” Journal of Universal Computer Science, vol. 8, pp. 705-717, 1998. 50. E. Pasalic and S.