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Generation and enumeration of all solutions of the characteristic sum condition

Shimon Even, Abraham Lempel
1972 Information and Control  
An algorithm for generating all proper words is given and a double recursion for their enumeration is described.  ...  A full tree is called compact if its corresponding prefix code has the property that the lexicographic ordering of its words corresponds to a nondecreasing ordering of the word lengths.  ...  ACKNOWLEDGMENTS The authors would like to thank Dr. Eugene Ott for suggesting the proof of (4) and Mr. Gideon Ehrlich for pointing out the generalization to the m-ary case. REcErwD: February 15, 1972  ... 
doi:10.1016/s0019-9958(72)90149-0 fatcat:mtpxgavxwfcazal5jstsfk32za

Weight distributions of linear codes and the Gleason-Pierce theorem

George T Kennedy
1994 Journal of combinatorial theory. Series A  
The ideas underlying the proof of the theorem yield necessary conditions on whether a solution to the MacWilliams identity can be the weight distribution of a linear code.  ...  Consequences of this result are an algebraic proof of the non-existence of an [16, 8, 6] f.s.d, binary even code, restrictions on distribution of cosets of codes, and occasional sharpening of upper bounds  ...  I also thank Thann Ward for introducing me to the subject of divisible codes, John Dillon for reading and commenting on a preliminary version of this paper, and Vera Pless for her time, effort, and advice  ... 
doi:10.1016/0097-3165(94)90004-3 fatcat:irh3kyfkdjdqxpm6pzk37vj5xi

Analogous programming with a template class library

Tibor Gregorics
2012 Teaching Mathematics and Computer Science  
In this paper, a template class library and its usage can be read. The classes of the library contain the C++ code of the algorithm of programming theorems.  ...  code can be written with inheritances, overriding virtual methods, composition of objectcs and template parameters.  ...  The optimist version checks whether the given condition holds on all elements of the enumeration.  ... 
doi:10.5485/tmcs.2012.0299 fatcat:mzwyghzphzh5letptqqeu6znom

Translates of linear codes over Z/sub 4/

A. Bonnecaze, I.M. Duursma
1997 IEEE Transactions on Information Theory  
For the particular case of quaternary Preparata codes, we obtain that the number of distinct complete weights for the dual Preparata codes and the number of distinct complete coset weight enumerators for  ...  the Preparata codes are both equal to ten, independent of the codelength.  ...  ACKNOWLEDGMENT The authors wish to thank P. V. Kumar and P. Solé for their interest in this work and for stimulating discussions.  ... 
doi:10.1109/18.605585 fatcat:qs2w4ubf4ffpfguvsimlz4k4q4

Page 45 of Mathematical Reviews Vol. 47, Issue 1 [page]

1974 Mathematical Reviews  
The author gives a solution to this problem, which is stated first in a special | case and then generally.  ...  The matrix A is said to be row stochastic [column stochastic] if each of the row [column] sums is | and is said to be doubly stochastic if each row sum and each column sum is 1. Using J. W.  ... 

Page 352 of Mathematical Reviews Vol. 45, Issue 2 [page]

1973 Mathematical Reviews  
Conditions for the existence of solutions and their representations are given, extending 1945 | results of W. E.  ...  1942-1947 summed over all characteristic roots. Evidently Sylvester’s definition gives only polynomials in A.  ... 

Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces

Benjamin A. Burton, Melih Ozlen
2012 ACM Transactions on Mathematical Software  
integer programming, both of which either compute the solution precisely or reduce it to two possible values, and (iii) a fast but limited precision integer programming algorithm that bounds the solution  ...  Our integer programming framework is general, with the potential for further applications in computational geometry and topology.  ...  The authors are grateful to the Queensland Cyber Infrastructure Foundation and RMIT University for the use of their high-performance computing facilities.  ... 
doi:10.1145/2382585.2382589 fatcat:yytdf6vlyvahvef63embrf6nxe

Efficient enumeration of solutions produced by closure operations [article]

Arnaud Mary, Yann Strozecki
2019 arXiv   pre-print
We also study the problem of generating minimal or maximal elements of closures and prove that some of them are related to well known enumeration problems such as the enumeration of the circuits of a matroid  ...  In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations.  ...  Acknowledgements The authors have been partially supported by the French Agence Nationale de la Recherche, AGGREG project reference ANR-14-CE25-0017-01 and we thank the members of the project and Mamadou  ... 
arXiv:1712.03714v3 fatcat:whvynvbgv5f3lgkmpj67pqnb5i

From Linear Codes to Hyperplane Arrangements via Thomas Decomposition [article]

Wilhelm Plesken, Thomas Bächler
2014 arXiv   pre-print
This yields both a generalization and a refinement of the weight enumerator of a linear code.  ...  We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial.  ...  In doing so, we define a generalization and a refinement of the weight enumerator of a linear code.  ... 
arXiv:1202.3625v2 fatcat:qslinrydnbhm5edt2buwmwbsvy

Page 333 of Geographical Analysis Vol. 34, Issue 4 [page]

2002 Geographical Analysis  
needed for the most general case of admitting any contiguous region as a possible solution.  ...  There is a “need for a tractable constraint form that captures all con- tiguous site patterns regardless of spatial characteristics” (Cova and Church 2000, p. 328).  ... 

Systematic Enumeration of Parallel Manipulators [chapter]

L. W. Tsai
1999 Parallel Kinematic Machines  
The classification is followed by an enumeration of the kinematic structures according to the degrees of freedom and connectivity listing.  ...  Abstract In this paper, a systematic methodology for enumeration of the kinematic structures of parallel manipulators is presented.  ...  The generator enumerates all possible solutions via a combinatorial analysis.  ... 
doi:10.1007/978-1-4471-0885-6_3 fatcat:yxho4n2vvfaxjf4q32eax3knqy

Page 2624 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
The second phase determines the optimal school districting that minimizes the sum of the distances traveled by all students.  ...  We prove that under certain conditions, with an increase in the dimensions of the system of equations, the solution of a Leontief model with random coefficients of direct costs converges to the solution  ... 

Page 22 of Mathematical Reviews Vol. 52, Issue 1 [page]

1976 Mathematical Reviews  
Namely, if L is a finite geometric lattice and if x is a modular flat of L, then the characteristic polynomial of [0, x] divides the characteristic polynomial of L.  ...  is the sum of the corresponding functions of the P;.  ... 

Efficient Enumeration of Solutions Produced by Closure Operations

Arnaud Mary, Yann Strozecki, Marc Herbstritt
2016 Symposium on Theoretical Aspects of Computer Science  
In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations.  ...  When the relation is over a domain larger than two elements, we prove that our generic enumeration method fails, since the associated decision problem is NP-hard.  ...  Authors have been partly supported by the ANR project Aggreg and we thank the members of the project and Mamadou Kanté for interesting discussions about enumeration.  ... 
doi:10.4230/lipics.stacs.2016.52 dblp:conf/stacs/MaryS16 fatcat:rn4wz3vugfdezd7nxs24tdnx4q

Complete weight enumerators of generalized Kerdock code and related linear codes over Galois ring

Aleksey Kuzmin, Aleksandr Nechaev
2001 Discrete Applied Mathematics  
It is a concatenation of some special (base) linear code over the Galois ring of characteristic 4 and Reed-Solomon code of dimension 2: Here the complete weight enumerators of Kerdock code, base linear  ...  Methods of proofs are based on the properties of trace function in Galois ring and quadrics over the ÿeld of characteristic 2.  ...  Acknowledgements The authors wish to thank Prof. V.T. Markov for the help in preparing of the manuscript and Referees for the helpful remarks.  ... 
doi:10.1016/s0166-218x(00)00348-6 fatcat:au3wnt4lzndqlowbqrdrnbn3n4
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