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This book that represents the author's Ph.D. thesis is devoted to applying symbolic methods to the problems of decoding linear codes and of algebraic cryptanalysis. The initial problems are reformulated in terms of systems of polynomial equations over a finite field, which solution(s) should yield a way to solve the initial problems. Solutions of such systems are obtained using Grobner bases. The first part is devoted to an application of system solving to decoding linear codes. The original method for arbitrary linear codes, which in some sense generalizes the Newton identities method, is...

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.