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Weight distribution of Preparata codes over Z_4 and the construction of 3-designs
《Science China Mathematics》2014年第6期1155-1162,共8页LI WeiXia SHEN Hao 
supported by National Natural Science Foundation of China(Grant No.11071163);Doctor Fund of Shandong Province(Grant No.BS2009SF017)
In this paper,we calculate the number of the codewords(with Hamming weight 7)of each type in the Preparata codes over Z4,then give the parameter sets of 3-designs constructed from the supports of the codewords of each...
关键词:T-DESIGNS weight distribution Preparata codes over Z4 
Lower bounds on the minimum distance in Hermitian one-point differential codes
《Science China Mathematics》2013年第7期1449-1455,共7页KORCHMROS Gábor NAGY Gábor Pétery 
financially supported by the TAMOP-4.2.1/B-09/1/KONV-2010-0005 project
Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at a...
关键词:AG code Weierstrass gap Hermitian curve 
Algebraic manipulation detection codes被引量:1
《Science China Mathematics》2013年第7期1349-1358,共10页CRAMER Ronald FEHR Serge PADRó Carles 
supported by the Singapore National Research Foundation(Grant No.NRF-CRP2-2007-03)
Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret shari...
关键词:CRYPTOGRAPHY keyless message authentication algebraic manipulation 
Linear recurring sequences and subfield subcodes of cyclic codes被引量:2
《Science China Mathematics》2013年第7期1413-1420,共8页GAO ZhiHan FU FangWei 
supported by National Key Basic Research Program of China(973 Program)(Grant No.2013CB834204);National Natural Science Foundation of China(Grant Nos.61171082 and 10990011)
Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurrin...
关键词:linear recurring sequences characteristic polynomial cyclic codes subfield subcodes trace codes 
Tensor products of ideal codes over Hopf algebras
《Science China Mathematics》2013年第4期737-744,共8页GARCíA-RUBIRA J.M. LóPEZ-RAMOS J.A. 
supported by projects MTM 2008-03339 from the Ministerio de Cienica e In,P07-FQM03128;FQM0211 from Junta de Andalucía and TEC 2009-13763-C02-02
We study indecomposable codes over a family of Hopf algebras introduced by Radford.We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes,extending the corresponding result that was pre...
关键词:Radford Hopf algebra ideal code tensor product of ideals 
Type Ⅱ codes over finite rings
《Science China Mathematics》2010年第1期203-212,共10页DOUGHERTY Steven T 
supported by National Natural Science Foundation of China (Grant No.10871079)
In this paper,we generalize the concept of Type Ⅱ codes to arbitrary finite rings. We focus on Type Ⅱ codes over finite chain rings and use the Chinese Remainder Theorem on these codes to study Type Ⅱ codes over pr...
关键词:FINITE principal IDEAL RINGS FINITE chain RINGS SELF-DUAL CODES TYPE  CODES 
A new combinatorial approach to the construction of constant composition codes
《Science China Mathematics》2008年第3期416-426,共11页YIN JianXing TANG Yu 
the National Natural Foundation of China (Grant Nos. 10671140, 10626038)
Constant composition codes(CCCs)are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the constr...
关键词:constant composition code optimal combinatorial approach CONSTRUCTION 05B05 94B25 
Difference packing arrays and systematic authentication codes
《Science China Mathematics》2004年第4期566-577,共12页YIN JianxingDepartment of Mathematics, Suzhou University, Suzhou 215006, China 
This work was supported in part by the National Natural Science Foundation of China(Grant No.13071086).
In this paper, a type of combinatorial design (called difference packing array)is proposed and used to give a construction of systematic authentication codes. Taking advantage of this construction, some new series of ...
关键词:AUTHENTICATION codes  DIFFERENCE PACKING arrays  constructions. 
Generalized Hamming weights and equivalences of codes被引量:2
《Science China Mathematics》2003年第5期690-695,共6页樊恽 刘宏伟 Lluis Puig 
The first two authors were supported by the 973 Basic Research P rogram of China.
It is proved that any linear isomorphism between two linear codes which preserves a generalizedHamming weight is a monomial equivalence, which is an extension of a theorem of MacWilliams.
关键词:equivalence  GENERALIZED Hamming weight  isometry. 
On the dual of quaternary Goethals codes and their weight hierarchies
《Science China Mathematics》2002年第11期1361-1371,共11页崔杰 万哲先 
Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goet...
关键词:QUATERNARY Goethals code  symmetrized WEIGHT enumerator  GENERALIZED Hamming weights. 
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