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Generation and enumeration of all solutions of the characteristic sum condition

1972
*
Information and Control
*

An algorithm for

doi:10.1016/s0019-9958(72)90149-0
fatcat:mtpxgavxwfcazal5jstsfk32za
*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 ...##
###
Weight distributions of linear codes and the Gleason-Pierce theorem

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 ...

##
###
Analogous programming with a template class library

2012
*
Teaching Mathematics and Computer Science
*

In this paper, a template class library

doi:10.5485/tmcs.2012.0299
fatcat:mzwyghzphzh5letptqqeu6znom
*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*. ...##
###
Translates of linear codes over Z/sub 4/

1997
*
IEEE Transactions on Information Theory
*

For

doi:10.1109/18.605585
fatcat:qs2w4ubf4ffpfguvsimlz4k4q4
*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. ...##
###
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

2012
*
ACM Transactions on Mathematical Software
*

integer programming, both

doi:10.1145/2382585.2382589
fatcat:yytdf6vlyvahvef63embrf6nxe
*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. ...##
###
Efficient enumeration of solutions produced by closure operations
[article]

2019
*
arXiv
*
pre-print

We also study

arXiv:1712.03714v3
fatcat:whvynvbgv5f3lgkmpj67pqnb5i
*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 ...##
###
From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
[article]

2014
*
arXiv
*
pre-print

This yields both a

arXiv:1202.3625v2
fatcat:qslinrydnbhm5edt2buwmwbsvy
*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. ...##
###
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]

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. ...

##
###
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

2016
*
Symposium on Theoretical Aspects of Computer Science
*

In this paper we address

doi:10.4230/lipics.stacs.2016.52
dblp:conf/stacs/MaryS16
fatcat:rn4wz3vugfdezd7nxs24tdnx4q
*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*. ...##
###
Complete weight enumerators of generalized Kerdock code and related linear codes over Galois ring

2001
*
Discrete Applied Mathematics
*

It is a concatenation

doi:10.1016/s0166-218x(00)00348-6
fatcat:au3wnt4lzndqlowbqrdrnbn3n4
*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. ...
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