Parametric restrictions on quasi-symmetric designs
نویسندگان
چکیده
In this paper, we attach several new invariants to connected strongly regular graphs (excepting conference on non-square number of vertices): one invariant called the discriminant, and a p-adic corresponding each prime p. We prove parametric restrictions quasi-symmetric 2-designs with given block graph G defect (absolute difference two intersection numbers) solely in terms parameters G, including these invariants. This is natural analogue Schutzenberger’s Theorem Shrikhande–Chowla–Ryser theorem. theorem effective when can be explicitly computed. do for complete multipartite graphs, co-triangular symplectic non-orthogonality (over field order 2) Steiner yielding explicit whose belong any four classes.
منابع مشابه
A note on quasi-symmetric designs
A quasi-symmetric design is a (v, k, λ) design with two intersection numbers x, y where 0 ≤ x < y < k. We show that for fixed x, y, λ with x > 1, λ > 1, y = λ and λ (4xy + ((y − x) − 2x− 2y + 1)λ) a perfect square of a positive integer, there exist finitely many quasi-symmetric designs. We rule out the possibilities of quasi-symmetric designs corresponding to y = x + 3 and (λ, x) = (9, 2), (8, ...
متن کاملMaximal arcs and quasi-symmetric designs
In 2001, Blokhuis and Haemers gave an interesting construction for quasisymmetric designs with parameters 2-(q, q(q − 1)/2, q(q − q − 2)/4) and block intersection numbers q(q − 2)/4 and q(q − 1)/4 (where q ≥ 4 is a power of 2), which uses maximal arcs in the affine plane AG(2, q) and produces examples embedded into affine 3-space AG(3, q). We consider this construction in more detail and in a m...
متن کاملPolarities, quasi-symmetric designs, and Hamada's conjecture
We prove that every polarity of PG(2k − 1, q), where k ≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to PGk(2k, q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. P...
متن کاملBinary codes and quasi-symmetric designs
obtain a new for the of a-(u, A) design the block intersection designs are eliminated by an ad hoc coding theoretic argument. A 2-(v, k, A) design 93 is said to be quasi-symmetric if there are two block intersection sizes s1 and s2. The parameters of the complementary design !3* are related to the parameters of 93 as follows: Here Ai denotes the number of blocks through a given i points (and A ...
متن کاملOn quasi-symmetric designs with intersection difference three
In a recent paper, Pawale [22] investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x+ 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper, quasi-symmetric designs with y−x = 3 are investigated. It is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2022
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2021.103434