Abstract
In this paper, it is first shown that the set of polynomials h α (X) such that β generates a normal basis of GF(q n) over GF(q), is a multiplicative group, in the algebra GF(q)[X]/(X n−1), if and only if there exists at least one Self Complementary Normal (SCN) basis. It is shown how the cyclic convolution product may be used to construct a normal basis from given normal bases. A method of construction of a SCN basis is then presented and compared with the construction of A.Lempel and M.Weinberger [4], A.Poli [8], C.C.Wang [12]
The authors wish to acknowledge Professor Alain Poli for suggestions and stimulating discussions.
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© 1995 Springer-Verlag Berlin Heidelberg
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Lacan, J., Delpeyroux, E. (1995). A note on normal bases. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_25
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DOI: https://doi.org/10.1007/3-540-60114-7_25
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