Weights of irreducible cyclic codes
LD Baumert, RJ McEliece - Information and control, 1972 - Elsevier
LD Baumert, RJ McEliece
Information and control, 1972•ElsevierWith any fixed prime number p and positive integer N, not divisible by p, there is associated
an infinite sequence of cyclic codes. In a previous article it was shown that a theorem of
Davenport-Hasse reduces the calculation of the weight distributions for this whole sequence
of codes to a single calculation (essentially that of calculating the weight distribution for the
simplest code of the sequence). The primary object of this paper is the development of
machinery which simplifies this remaining calculation. Detailed examples are given. In …
an infinite sequence of cyclic codes. In a previous article it was shown that a theorem of
Davenport-Hasse reduces the calculation of the weight distributions for this whole sequence
of codes to a single calculation (essentially that of calculating the weight distribution for the
simplest code of the sequence). The primary object of this paper is the development of
machinery which simplifies this remaining calculation. Detailed examples are given. In …
With any fixed prime number p and positive integer N, not divisible by p, there is associated an infinite sequence of cyclic codes. In a previous article it was shown that a theorem of Davenport-Hasse reduces the calculation of the weight distributions for this whole sequence of codes to a single calculation (essentially that of calculating the weight distribution for the simplest code of the sequence). The primary object of this paper is the development of machinery which simplifies this remaining calculation. Detailed examples are given. In addition, tables are presented which essentially solve the weight distribution problem for all such binary codes with N < 100 and, when the block length is less than one million, give the complete weight enumerator.
Elsevier
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