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【期刊论文】CONJUGATE ORTHOGONAL DIAGONAL LATIN SQUARES WITH MISSING SUBSQUARES
杜北梁, Frank E. Bennett, Beiliang Du, Hantao Zhang
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-1年11月30日
We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate, and the latter is also a diagonal Latin square, as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS with a missing sub-square. The main purpose of this paper is two-fold. First of all, we show that for any positive integers n ≥ 1, a CODLS of order v with a missing subsquare of order n exists if v ≥ 13n/4 + 93 and v − n is even. Secondly, we show that for 2 ≤ n ≤ 6, a CODLS of order v with a missing subsquare of order n exists if and only if v ≥ 3n+2 and v − n is even, with one possible exception.
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【期刊论文】Splitting Balanced Incomplete Block Designs with Block Size 3
杜北梁, Beiliang Du
Published online 22 June 2004 in Wiley InterScience,-0001,():
-1年11月30日
Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (v, 3k, λ)-splitting BIBDs; we give the spectrum of (v, 3 × 2, λ)-splitting BIBDs. As an application, we obtain an infinite class of 2-splitting A-codes.
splitting balanced incomplete design, k-splitting A-code
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【期刊论文】α- Resolvable Group Divisible Designs with Block Size Three
杜北梁, Yan Zhang, Beiliang Du
Published online 16 August 2004 in Wiley InterScience,-0001,():
-1年11月30日
A group divisible design GD (k, λ, t; tu ) isα-resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely α blocks in each class. The necessary conditions for the existence of such a design are λt( u – 1) = r ( k – 1) , bk=rtu; k│αtu andα│ r. It is shown in this paper that these conditions are also sufficient when k =3, with some definite exceptions.
group divisible, design, resolvable, frame
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【期刊论文】The existence of orthogonal diagonal Latin squares with subsquares
杜北梁, B. Du
B. Du. Discrete Mathematics 148 (1996) 37-48,-0001,():
-1年11月30日
We prove that there exists a pair of orthogonal diagonal Latin squares of order v with missing subsquares of side n (ODLS (v, n ) for all v≥3n+2 and v-n even. Further, there exists a magic square of order v with missing subsquare of side n (MS (v, n)) for all v≥3n+2 and v-neven.
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【期刊论文】The existence of three idempotent IMOLS
杜北梁, R. Julian R. Abel, Beiliang Du
R. J. R. Abel. B. Du. Discrete Mathematics 262 (2003) 1-16,-0001,():
-1年11月30日
In this paper it is shown that an idempotent TD (5, m) − TD (5, n) exists whenever the known necessary condition m ≥ 4n+1 is satis3ed, except when (m, n)=(6, 1) and possible when (m, n)=(10, 1). For m < 60 and n ≤ 10, we also indicate where several idempotent TD(k, m)−TD(k, n)’s for k = 6, 7 can be found.
Transversal design, Incomplete transversal design, Idempotent incomplete transversal design, Quasi-difference matrix, Orthogonal latin squares, Incomplete orthogonal latin square
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