361 research outputs found
Cyclotomic Constructions of Skew Hadamard Difference Sets
We revisit the old idea of constructing difference sets from cyclotomic
classes. Two constructions of skew Hadamard difference sets are given in the
additive groups of finite fields using unions of cyclotomic classes of order
, where is a prime and a positive integer. Our main tools
are index 2 Gauss sums, instead of cyclotomic numbers.Comment: 15 pages; corrected a few typos; to appear in J. Combin. Theory (A
Cyclotomic Constructions of Cyclic Codes with Length Being the Product of Two Primes
Cyclic codes are an interesting type of linear codes and have applications in
communication and storage systems due to their efficient encoding and decoding
algorithms. They have been studied for decades and a lot of progress has been
made. In this paper, three types of generalized cyclotomy of order two and
three classes of cyclic codes of length and dimension
are presented and analysed, where and are two distinct primes.
Bounds on their minimum odd-like weight are also proved. The three
constructions produce the best cyclic codes in certain cases.Comment: 19 page
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