Trace-Function on a Galois Ring in Coding Theory
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
IEEE Transactions on Information Theory
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A classical binary Preparata code P"2(m) is a nonlinear (2^m^+^1,2^2^(^2^^^m^-^1^-^m^),6)-code, where m is odd. It has a linear representation over the ring Z"4 [Hammons et al., The Z"4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory 40(2) (1994) 301-319]. Here for any q=2^l2 and any m such that (m,q-1)=1 a nonlinear code P"q(m) over the field F=GF(q) with parameters (q(@D+1),q^2^(^@D^-^m^),d=3q), where @D=(q^m-1)/(q-1), is constructed. If d=3q this set of parameters generalizes that of P"2(m). The equality d=3q is established in the following cases: (1) for a series of initial admissible values q and m such that q^m