Relative (pn,p,pn,n)-difference sets with GCD(p,n)=1

Feng, Tao

doi:10.1007/s10801-008-0124-5

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…Note that the parameters in (1.5) do not satisfy (1.4) either since n = p + 1 and min r∈π (m) {ν r (m)} = p + 1 (here p = 2 or p is a Mersenne prime). Very recently the first author [8] gave a construction of (p(p + 1), p, p(p + 1), p + 1) abelian RDS, where p is a Mersenne prime. But the parameters of these RDS still do not satisfy (1.4).…”

Section: Theorem 12 (Seementioning

confidence: 99%

“…These non-existence results suggest that in order to use Theorem 1.2 to construct more MUB than the minimum in (1.3), one has to go beyond the simple parameter sets considered above. Some investigations in this direction were carried out by Feng [8]. On the construction side, we construct a family of (4q, q, 4q, 4) non-abelian RDS, where q is an odd prime power greater than 9, q ≡ 1 (mod 4).…”

Section: Theorem 12 (Seementioning

confidence: 99%

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Semi-regular relative difference sets with large forbidden subgroups

Feng

Xiang

2008

Journal of Combinatorial Theory, Series A

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Relative difference set Semi-regular relative difference set Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters (m, n, m, m/n) in groups of non-prime-power orders. Let p be an odd prime. We prove that there does not exist a (2p, p, 2p, 2) relative difference set in any group of order 2p 2 , and an abelian (4p, p, 4p, 4) relative difference set can only exist in the group Z 2 2 × Z 2 3 . On the other hand, we construct a family of non-abelian relative difference sets with parameters (4q, q, 4q, 4), where q is an odd prime power greater than 9 and q ≡ 1 (mod 4). When q = p is a prime, p > 9, and p ≡ 1 (mod 4), the (4p, p, 4p, 4) non-abelian relative difference sets constructed here are genuinely non-abelian in the sense that there does not exist an abelian relative difference set with the same parameters.

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Section: Theorem 12 (Seementioning

confidence: 99%

Section: Theorem 12 (Seementioning

confidence: 99%

Semi-regular relative difference sets with large forbidden subgroups

Feng

Xiang

2008

Journal of Combinatorial Theory, Series A

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“…For subsets The following result is a variation of Lemma 2 in [10], and the proof is almost the same with the one there with only minor modifications.…”

Section: Group Ring Codes Over Finite Fieldsmentioning

confidence: 83%

On self-orthogonal group ring codes

Feng

2008

Des. Codes Cryptogr.

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We obtain structural results about group ring codes over F [G], where F is a finite field of characteristic p > 0 and the Sylow p-subgroup of the Abelian group G is cyclic. As a special case, we characterize cyclic codes over finite fields in the case the length of the code is divisible by the characteristic of the field. By the same approach we study cyclic codes of length m over the ring R = F q [u], u r = 0 with r > 0, gcd(m, q) = 1. Finally, we give a construction of quasi-cyclic codes over finite fields.

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“…In Feng (2007), T. Feng constructed, (q n−2 , q, q n−2 , q n−3 )-difference sets in a subgroup of SL(n, q) of order q n−1 . Assume q = p is an add prime and set n = 4, g(x, y) = ax 2 + bx + cy (a, b, c ∈ Z p ).…”

Section: Case I -Product Typementioning

confidence: 99%

“…Applying methods of Davis (1991) and Davis (1992) we can also construct such difference sets in Z 3 p . Moreover, as a special case of Feng (2007) we know that there are also such difference sets in Z 3 p . In this article we study (p 2 , p, p 2 , p)difference sets in Z 3 p and classify these classes into two typical types.…”

Section: Introductionmentioning

confidence: 99%