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- W62003129 abstract "GF( p 2 )is a vector space of dimension two over GF( p ). We study in this paper the consequences of this fact. Necessary and sufficient conditions are given for a code on GF( p 2 )to be a p -code (generator matrix consisting of elements from GF( p )), unreal code (code over GF( p 2 ), the only codeword consisting of elements from GF( p ) is 0). We study C , , Re( C ) (the real set of C ), and C 0 (the subfield subcode of the codewords of C which have components from GF( p )). We show how to find the generators of Re( C ) and C o when we know the generator of the cyclic code C over GF( p 2 ). The idempotents and quadripotents, — q 2 ( x ) ≠ q ( x ) and q 4 ( x ) = q ( x ) — of binary cyclic codes are studied. The existence of quadripotents in a binary cyclic code is a necessary and sufficient condition for a binary cyclic code to be the real set of a code over GF(4) which is not a 2-code, namely, a code, a generator matrix of which consists of O's and ľs." @default.
- W62003129 created "2016-06-24" @default.
- W62003129 creator A5066897845 @default.
- W62003129 date "1983-01-01" @default.
- W62003129 modified "2023-09-27" @default.
- W62003129 title "Cyclic Codes Over Gf(4) and Gf(2)" @default.
- W62003129 doi "https://doi.org/10.1016/s0304-0208(08)73394-2" @default.
- W62003129 hasPublicationYear "1983" @default.
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