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Title:
A General Theory of Codes Abstract: Recent developments in cryptography have led to a general theory of codes. It provides a unified treatment of cryptographic topics such as secure log-in, cryptosystem codes, key exchange schemes and secret sharing schemes, as well as of topics from outside of cryptography, such as error control codes, data compression codes, finite codes, infinite codes, quantum codes, genetic codes and other objects. The general theory is unavoidably algebraic/logical, after the fashion of A. I. Mal'cev's definition of an algebraic system. There are natural notions of subcodes, product codes, quotient codes, types of duality for codes, and types of morphisms of codes. Codes obey the three standard isomorphism theorems of universal algebra [1]. This suggests that there may be a Jordan-Hoelder-Schreier theorem for codes. [1] G. R. Blakley and I. Borosh, A general theory of codes, II, in Information Security: ISW '97 Proceedings, E. Okamoto, G. Davida and M. Mambo (Editors), Volume 1396 of Lecture Notes in Computer Science, Springer-Verlag, Berlin (1998), pp. 1 - 31. |