Download Coding and Cryptography by T. Korner PDF

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By T. Korner

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Extra resources for Coding and Cryptography

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B) Show that extension and truncation do not change the size of a code. Show that it is possible to puncture a code without reducing the information rate. (c) Show that the minimum distance of the parity extension C + is the least even integer n with n d(C ). Show that the minimum distance of C ; is d(C ) or d(C ) ; 1. Show that puncturing does not change the minimum distance. 10. If C1 and C2 are of appropriate type with generator matrices G1 and G2 write down a generator matrix for C1jC2. 11.

Kline Mathematical Thought from Ancient to Modern Times OUP, 1972. 5] N. Koblitz A Course in Number Theory and Cryptography Springer, 1987. 6] D. E. Knuth The Art of Computing Programming Addison-Wesley. The third edition of Volumes I to III is appearing during this year and the next (1998{9). 7] G. M. Goldie and R. G. E. Pinch Communication Theory CUP, 1991. 8] T. M. Thompson From Error-correcting Codes through Sphere Packings to Simple Groups Carus Mathematical Monographs 21, MAA, Washington DC, 1983.

The real di culty lies in the necessity for sharing the secret sequence k. If a random sequence is reused it ceases to be random (it becomes `the same code as last Wednesday' or the `the same code as Paris uses') so, when there is a great deal of code tra c, new one-time pads must be sent out. If random bits can be safely communicated so can ordinary messages and the exercise becomes pointless. In practice we would like to start from a short shared secret `seed' and generate a ciphering string k that `behaves like a random sequence'.

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