Báo cáo toán học: "New symmetric designs from regular Hadamard matrices" pdf

... regular Hadamard matrix of order 4 and H is a regular Hadamard matrix of order 9 · 4 d+1 . Therefore, one can obtain a family of regular Hadamard matrices of order 9 · 4 d , starting with a regular ... Yamada, Hadamard matrices, sequences, and block designs, in Contemporary Design Theory, eds. J.H. Dinitz and D.R. Stinson, John Wiley & Sons, 1992, 431–560. New symmetric...

Ngày tải lên: 07/08/2014, 06:22

... R. Omidi and B. Tayfeh-Rezaie, 3 -Designs from P SL(2, q), Dis- crete Math. 306 (2006), 3063–3073. [3] P. J. Cameron, G. R. Omidi and B. Tayfeh-Rezaie, 3 -Designs from PGL(2, q), Elec- tron. J. Comb. ... infinite family of 3 -designs from Preparata codes over Z 4 , Des. Codes Cryptogr. 15 (1998), no. 2, 175–181. [6] T. Helleseth, C. Rong, K. Yang, New infinite families of 3 -designs...

Ngày tải lên: 07/08/2014, 15:22

... Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. New proofs of Schur-concavity for a class of symmetric ... three theorems, we need the following lemmas. Lemma 1. [1, p. 67],[2] If ϕ is symmetric and convex (concave) on symmetric convex set Ω, then ϕ is Schur-convex (Schur-concav...

Ngày tải lên: 20/06/2014, 21:20

... that an element a in R is said to be (von Neumann) regular if a = aba for some b ∈ R. A subset X ⊆ R is said to be regular if every element in X is regular. Proposition 3.5. The following are equivalent ... defined similarly. Recall that a ring R is said to be semiregular in case R/J is regular and idempotents can be lifted modulo J. R is a right weakly continuous ring if R is semiregu...

Ngày tải lên: 06/08/2014, 05:20

... here for the sake of completeness. Let L be prime and consider the field of L elements, numbered from 0 to L − 1. Associate each field element with a vertex of K L . We require that 3 divides L ... 137. Finally, using R(3, 3, 6) ≥ 54, R(3, 3, 7) ≥ 72, R(3, 3, 9) ≥ 110, and R(3, 3, 11) ≥ 138 all from [SLZL], we get the lower bounds R(3, 3, 3, 6) ≥ 165, R(3, 3, 3, 7) ≥ 220, R(3, 3, 3, 9) ≥ 33...

Ngày tải lên: 07/08/2014, 06:20

... distance two from each other. In Case A (resp., B3b), we produced an element of L ≥3 \ C, c3 (resp., e6), at Euclidean distance 3 (resp., √ 10) from our starting point f3 ∈ C  2 .InCaseA,apart from ... element of C  2 at Euclidean distance 3 from c3isz3. In Case B3b, apart from f3, the only possible locations for an element of C  2 at Euclidean distance √ 10 from e6ared9andf9,...

Ngày tải lên: 07/08/2014, 06:20

... unexpected way. First, we discovered a simple way to construct families of (k, g)-graphs from those of k -regular graphs of girth at least g. Applying this construction to the graphs CD(2 g+1 2  ... which asserts that the orders of k- regular graphs of girth at least g provide upper bounds on the orders of (k, g)-cages. Namely, Theorem 2.1 [7] Let G be a k -regular graph of girth at l...

Ngày tải lên: 07/08/2014, 06:22

... electronic journal of combinatorics 5 (1998), # R39 9 Proof: Consider the 2 βn vectors A  B constructed from the 2 βn pairs with | A∩B |= tn. Clearly each such vector will contain tn ∗’s, (p−t)n 1’s, (p−t)n ... −p 2 )(0≤p≤ 1). Consider the random variable X = A ∪ B with A, B chosen uniformly and independently from F .SinceFis strongly union-free X will take on 2 [2α+o(1)]n distinct value...

Ngày tải lên: 07/08/2014, 06:22

... O(1/n 2 ). Roth published in 1951 [14] an upper bound H n = O(1/n √ log log n) and a construction from P. Erd˝os which shows that H n is not of lower order than n −2 , so that if the conjecture ... the main parameters are: ini- tial temperature T 0 =0.01; number of temperature changes, N max , from 100 to 1000; maximum number of iterations for a given temperature runLimit = 1000n;numberof...

Ngày tải lên: 07/08/2014, 06:23

... ,r.Letk 1 ≥ 3. Define graphs G i , i =1, 2, ,k 1 − 1, with |V (G i )| = |V (G)| on distinct vertices (from each other), each with the coloring φ.LetH bethecompletegraph on the vertices V (H)=∪ k 1 −1 i=1 V ... ,k r ), the electronic journal of combinatorics 9 (2002), #R13 4 Definition 2.3 We say that the n × n symmetric matrix T = T(x 0 ,x 1 , ,x r )=(a ij ) 1≤i,j≤n is a Ramsey incidence mat...

Ngày tải lên: 07/08/2014, 06:23