Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The 25 revised full papers presented here together with 7 invited papers address subjects such as block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.
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This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999.The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.
\ \ \ On bent and highly nonlinear balanced/resilient functions and their algebraic immunities\ 1\ \ \ \ On generalized parity checks\ 29\ \ \ \ Cryptography based on bilinear maps\ 35\ \ \ \ The merit factor problem for binary sequences\ 51\ \ \ \ Quantum period reconstruction of binary sequences\ 60\ \ \ \ The vector key equation and multisequence shift register synthesis\ 68\ \ \ \ A general framework for applying FGLM techniques to linear codes\ 76\ \ \ \ A theory of highly nonlinear functions\ 87\ \ \ \ The solutions of the third power sum equation for Niho type decimations\ 101\ \ \ \ On constructing AG codes without basis functions for Riemann-Roch spaces\ 108\ \ \ \ Computing Grobner bases for vanishing ideals of finite sets of points\ 118\ \ \ \ A class of fermat curves for which Weil-Serre's bound can be improved\ 128\ \ \ \ Nonbinary quantum codes from hermitian curves\ 136\ \ \ \ A genetic algorithm for cocyclic Hadamard matrices\ 144\ \ \ \ Unconditionally secure chaffing-and-winnowing : a relationship between encryption and authentication\ 154\ \ \ \ A fast calculus for the linearizing attack and its application to an attack on KASUMI\ 163\ \ \ \ On achieving chosen ciphertext security with decryption errors\ 173\ \ \ \ Applying Fujisaki-Okamoto to identity-based encryption\ 183\ \ \ \ A short random fingerprinting code against a small number of pirates\ 193\ \ \ \ A general formulation of algebraic and fast correlation attacks based on dedicated sample decimation\ 203\ \ \ \ Traitor tracing against powerful attacks using combinatorial designs\ 215\ \ \ \ New bounds on the capacity of multi-dimensional RLL-constrained systems\ 225\ \ \ \ LDPC codes for fading channels : two strategies\ 235\ \ \ \ Low-floor tanner codes via Hamming-node or RSCC-node doping\ 245\ \ \ \ Algebraic constructions of quasi-cyclic LDPC codes - part I : for AWGN and binary random erasure channels\ 255\ \ \ \ Algebraic construction of quasi-cyclic LDPC codes - part II : for AWGN and binary random and burst erasure channels\ 265\ \ \ \ New constructions of quasi-cyclic LDPC codes based on two classes of balanced incomplete block designs : for AWGN and binary erasure channels\ 275\ \ \ \ Long extended BCH codes are spanned by minimum weight words\ 285\ \ \ \ On the Feng-Rao bound for generalized Hamming weights\ 295\ \ \ \ Nested codes for constrained memory and for dirty paper\ 307\ \ \ \ Complementary sets and Reed-Muller codes for peak-to-average power ratio reduction in OFDM\ 317\ \ \ \ Hadamard codes of length 2[superscript t]s (s odd) : rank and kernel\ 328\ \
