Báo cáo toán học: "Lower Bounds for q-ary Codes with Large Covering Radius" ppsx

... code C for a graph G = (V, E). Let c, c ′ ∈ C be distinct. If I r (v) = {c, c ′ } for some v ∈ V (G) we say that 1. c ′ forms a pair (with c) and 2. v witnesses a pair (that contains c). For c ... General bounds for identifying codes in some infinite regular graphs. Electron. J. Combin., 8(1):R3 9, 2001. [2] Ir`ene Charon, Olivier Hudry, and Antoine Lobstein. Identifying codes...

Ngày tải lên: 08/08/2014, 12:22

... subset C ⊂ F n 3 is called a ternary code with covering radius (at most) one, if ∀λ ∈ F n 3 ∃µ ∈ C with d(λ, µ) ≤ 1 (1) holds. For a monograph on covering codes see [1]. The problem to determine ... ternary code with covering radius one and k = n − 3. We set B i = {σ ∈ F k 3 : n σ = i} for i = 0, 1, B = B 0 ∪ B 1 and K i = {L ∈ L : |L ∩ B| = i} for 0 ≤ i ≤ 3. Let c be a co...

Ngày tải lên: 07/08/2014, 15:22

... that for every j ∈ [l + d −1], F j shares no edge with {f} ∪  i<j F i . From this, together with the occurrence of E 3 we get that for all j ∈ [l + d −1], F j shares exactly 2 vertices with ... S for j ∈ [d − 1]. We count the number of choices for G j : There are O(d) possible choices for an edge g ∈ {f} ∪  i<j G i for which G j is in Λ(g, 1); There are at most n v H...

Ngày tải lên: 07/08/2014, 21:21

... (i) and (iv) P 3 ∩ P 4 = {x} with x ∈ Z 6 . Let R denote a set the electronic journal of combinatorics 16 (2009), #R133 5 Lower Bounds for q-ary Codes with Large Covering Radius Wolfga ng Haas Immanuel ... the case k = 5. For k > 5 the computational effort became too la r ge for a systematical treatment. Here we got only a few sporadic new bounds: six bounds for k =...

Ngày tải lên: 08/08/2014, 01:20

... G be a CF-graph with minimum degree at least 3, Then the average genus γ avg (G) is larger than c log(β(G)) for some constant c > 0. In [9], we obtained the following result for the maximum ... CF-graph with minimum degree at least 3. Then lower bounds on the maximum genus are given in Table 1. The rows correspond to edge- connectivity k = 1 or k  2, respectively. The same boun...

Ngày tải lên: 08/08/2014, 12:23

... Z´emor: New bounds for codes identifying vertices in graphs, Electronic Journal of Combinatorics, vol. 6(1), R19, 1999. [7] G. Cohen, I. Honkala, A. Lobstein, G. Z´emor: Bounds for codes identifying ... D(G S ,r) ≤          2 5r for r even, 2r 5r 2 − 2r +1 for r odd. For the triangular lattice: 2 6r +3 ≤ D(G T ,r) ≤          1 2r +4 for r ≡ 0mod4, 1 2r +2...

Ngày tải lên: 07/08/2014, 06:22

... (a, b) < S(a, b) = M 2 (a, b) for all a, b > 0 with a = b. Seiffert [1] proved that inequalities A(a, b) < T (a, b) < S(a, b) hold for all a, b > 0 with a = b . Chu et al. [5] found ... convex combination bounds of Seiffert and geometric means for the arithmetic mean. J. Math. Inequal. 5(3), 429–434 (2011) [8] Liu, H, Meng, X-J: The optimal convex combination bound...

Ngày tải lên: 20/06/2014, 21:20

... case for the square grids and for the rest of this section we shall bound  ≥3 from below as tightly as we can. 2.2 Partitioning C We partition the code C into two subcodes C  and C  ,withC  consisting ... of degree zero. Since, by symmetry, one element in C  2 produces two vertices with degree zero or New Bounds for Codes Identifying Vertices in Graphs G´erard Cohen cohen@i...

Ngày tải lên: 07/08/2014, 06:20

... →∞,h(x i )→H(2p i − p 2 i ). Therefore we have [2α − β(p)+o(1)]n ≤ n  i=1 H(2p i − p 2 i ) ≤ nφ(p) (since pn =  p i ). Therefore αn ≤ 1 2 [β(p)+φ(p)+o(1)]n. New Bounds for Union-free Families of Sets Don ... B  disagreed with A  , C  agreed with either B  or A  , and the choice of D  is forced. The total number of choices on this triplet is 3 × 1 ×1 × 1+3×2×2×1=15. Values on t...

Ngày tải lên: 07/08/2014, 06:22

... either a red K m,m or a green K n,n . We obtain asymptotic bounds for b (m, n ) for m ≥ 2 fixed and n → ∞. 1 Introduction Recent exact results for bipartite Ramsey numbers [4] have rekindled interest ... Thomason in [7]. Note that b ( m, m ) = R (m, m ). In this note, we obtain asymptotic bounds for b ( m, n ) with m fixed and n → ∞. 2 The Main Result Theorem 1. Let m ≥ 2 be fixed....

Ngày tải lên: 07/08/2014, 06:22