Topic Generation of Matrices for Determining Minimum Distance and Decoding non-cyclic goppa codes

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– A simple method based on Newton’s identities arid

their
extensions is presented for determining the actual

minimum distance of
cyclic codes. More significantly, it is shown that this

method also provides
a mechanism for generating the type of syndrome

matrices needed by
Feng and Tzeng’s new procedure for decoding

cyclic and BCH codes up
to their actual minimum distance. Two procedures

for generating such
matrices are given. With these procedures, we have

generated syndrome
matrices having only one class of conjugate

syndromes on the minor
diagonal for all binary cyclic codes of length n < 63 and manly codes of length 63 5 n 5 99. A listing of such syndrome matrices for selected codes of length R < 63 is included. An interesting connection of the method presented in this correspondence to the shifting technique of . can you prepare a new paper for publication , i think work on generation matrices for non-cyclic goppa code be an idea for further work.

 

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