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对两类组合设计的探讨

Discussion on Two Types of Combinatorial Designs
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摘要 组合设计理论是组合数学的一个重要分支,在密码与编码中有广泛的应用.文献[1]定义了两种新的组合设计:外差族(EDF)和外平衡不完全区组设计(EBIBD),但是该文献并没有对它们做出详细的研究.给出在整环上EBIBD的一个构造,并通过补设计的方法由EBIBD构造一个对称平衡不完全区组设计(BIBD),证明了一类EBIBD与拉丁方的等价性;最后讨论了在自同构意义下EBIBD的一些性质,以及EDF与EBIBD之间的联系. Combinatorial designs is an important branch of Combinatorial mathematicas, and it is widely used in cryptography and coding theory [ 1], introduces two new types of combinatorial designs, which are called External difference family（EDF） and External balanced incomplete block design（EBIBD）, but it does not give detailed research on these two designs. This paper presents a construction to EBIBD and uses EBIBD to construct symmetric BIBD by complementary design, it also proves an equivalence between some special EBIBD and Latin Square;Finaly, we discuss the automorphism property of EBIBD and the relationship between EDF and EBIBD.
作者 陈群山 吴武顺
机构地区 漳州师范学院计算机科学与工程系
出处 《漳州师范学院学报（自然科学版）》 2007年第4期31-36,共6页 Journal of ZhangZhou Teachers College（Natural Science)
基金 漳州师院科研基金资助项目(SK05012)
关键词 组合设计 差族 平衡不完全区组设计 自同构 combinatorial designs difference family BIBD automorphism
分类号 O157.2 [理学—基础数学]
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参考文献9

  • 1W. Ogata, K. Kurosawa, D. R. Stinson, H. Saido. New combinatorial designs and their application to authentication codes and secret sharing schemes [J]. Discrete Mathematics, 2004, 279(1-3): 383-405.
  • 2C.J. Colboum, L H. Dinitz(Eds.). CRC Handbook of Combinatorial Designs [M]. Boca Raton: CRC Press, 1996.
  • 3T. Beth, D. Jungnickel and H. Lenz. Design Theory [M]. London: Cambridge University Press, 1986.
  • 4H. Hanani. Balanced incomplete block, designs and related designs [J]. Discrete Math., 1975, (11): 255-369.
  • 5M. Jimbo. Recursive constructions for cyclic BIB designs and their generalizations[J]. Discrete Math., 1993, (116): 79-95.
  • 6D. Jungnickel. Difference sets [C]. Contemporary desig.n theory, eds. by J. H. Dinitz and D. R. Stinson, John Wiley & Sons, 1992.
  • 7R. M. Wilson. Cyclotomy and difference families in elementary abelian groups [J]. J. Number Theory, 1972, (4): 17-47.
  • 8陈群山,曾吉文.两类组合设计及其在认证码中的应用[J].数学研究,2007,40(2):211-216. 被引量：1
  • 9徐明曜.有限群导引[M].北京:科学出版社,1999.54-61.

二级参考文献14

  • 1Ogata W,Kurosawa K,Stinson D R,Saido H.New Combinatorial Designs and Their Application to Authentication Codes and Secret Sharing Schemes.Discrete Mathematics,2004,(279):383-405.
  • 2Beth T,Jungnickel D,Lenz H.Design Theory.London:Cambridge University Press,1986.
  • 3Colbourn C J,Dinitz J H.CRC Handbook of Combinatorial Designs.CRC Press,Boca Raton,FL,1996.
  • 4Bose R C,Shrikhande S S,Parker E T.Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecrure.J.Math.,1960,(12):189-203.
  • 5Gilbert E N,Macwilliams F J,Sloane N J.Codes which Detect Deception.Bell System Technical Journal,1974,(53):405-424.
  • 6Simmons G J.Authentication Theory/Coding Theory.Advances in Cryptology-Crypto'84.Berlin:Springer-Verlag,1985,411-431.
  • 7Stinson D R.The Combinatorics of Authentication and Secrecy Codes.J.Cryptology,1990,(2):23-49.
  • 8Stinson D R.Combinatorial Charaterizations of Authentication Codes.Designs,Codes and Cryptography,1992,(2):175-187.
  • 9Wan Z X.Constuction of Cartesian Authentication Codes from Unitary Geometry.Designs,Codes and Cryptography,1992,(2):333-356.
  • 10De Soete M.New Bounds and Constructions for Authentication/Secrecy Codes with Splitting.J.Cryptology,1991,(3):173-186.

共引文献50

漳州师范学院学报（自然科学版）
2007年 第4期

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