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TR01-002 | 6th December 2000 00:00

Constructions of Codes from Number Fields


Authors: Venkatesan Guruswami
Publication: 4th January 2001 18:20
Downloads: 3220


We define number-theoretic error-correcting codes based on algebraic
number fields, thereby providing a generalization of Chinese Remainder
Codes akin to the generalization of Reed-Solomon codes to
Algebraic-geometric codes. Our construction is very similar to
(and in fact less general than) the one given by (Lenstra 1986), but
the parallel with the function field case is more apparent,
since we only use the non-archimedean places for the encoding.
We prove that over an alphabet size as small as 19, there even exist
asymptotically good number field codes of the type we consider.
This result is based on the existence of certain number
fields that have an infinite class field tower in which some primes of
small norm split completely.

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