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This thesis, develipes a fast alsgroitm for computing inverses in GF (2**m) using the normal basis of the field. The fast algorithm requires (q+p-1) muitiplions; where q=Int (log 2 (m-1)) and p is the number of 1's in the binary expression of (m-1). Therefore, the computing complexity is O (mlog-2(m)). The operatiou of the new algorithm is regular. simple, modular hence it is well-suited for VLSI implementation.
Generally, in the procedures of encoding and decodig in error control code, data are represented using conventional basis. However. computing inverses are required in most of decoding procedures of algebraic codes. Therefore, conventional encoding and decoding methods have the following drawbacks: (1) computing invcrses using conventional basis are complexity; or (2) basis transforms are required before and after each inverse computation. lu this thesis. we claim that the decoding computaton can be simplied if all data are represented by normal basis in the procedures of algebraic encoding and decoding. The new idea has been proved by means of computer simulation.
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