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1.

図書
図書
1. Sphere packings, lattices and groups. 3rd ed
J.H. Conway, N.J.A. Sloane ; with additional contributions by E. Bannai ... [et al.]
出版情報: New York ; Tokyo : Springer, c1999  lxxiv, 703 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 290
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2.

図書
図書
2. Covering codes
Gérard Cohen ... [et al.]
出版情報: Amsterdam ; Tokyo : Elsevier Science, 1997  xxi, 542 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 54
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目次情報: 続きを見る
Introduction
Covering problems
Applications
Basic Facts
Codes
The MacWilliams identities
Krawtchouk polynomials
Hamming spheres
Finite fields
Families of error-correcting codes
Designs, constant weight codes, graphs
Constructions
Puncturing and adding a parity check bit
Direct sum
Piecewise constant codes
Variations on the (u, u + v) construction
Matrix construction
Cascading
Optimal short nonbinary codes
Simulated annealing and local search
Normality
Amalgamated direct sum
Normality of binary linear codes
Abnormal binary nonlinear codes
Normality of binary nonlinear codes
Blockwise direct sum
Linear Constructions
Basic facts about linear covering codes
The case R=1; examples of small codes
Saving more than one coordinate
Davydov's basic construction
Lower Bounds
Bounds for the cardinality of the union of K spheres
Balanced codes
Excess bounds for codes with covering radius one
Excess bounds for codes with arbitrary covering radius
The method of linear inequalities
Table on K(n,R)
Lower bounds for nonbinary codes
Lower Bounds for Linear Codes
Excess bounds for linear codes
Linear codes with covering radius two and three
Tables for linear codes
Upper Bounds
Codes with given size and distance
Covering radii of subcodes
Covering radius and dual distance
Reed-Muller Codes
Definitions and properties
First order Reed-Muller codes
Reed-Muller codes of order 2 and m-3
Covering radius of Reed-Muller codes of arbitrary order
Algebraic Codes
BCH codes: definitions and properties
2- and 3-error-correcting BCH codes
Long BCH codes
Normality of BCH codes
Other algebraic codes
Perfect Codes
Perfect linear codes over IF q
A nonexistence result
Enumeration of perfect binary codes
Enumeration of perfect codes over IF q
Mixed codes
Generalizations of perfect codes
Asymptotic Bounds
Covering radius of unrestricted codes
Greedy algorithm and good coverings
Covering radius of linear codes
Density of coverings
Coverings of small size
Bounds on the minimum distance
Covering radius as a function of dual distance
Packing radius vs covering radius
Weighted Coverings
Basic notions
Lloyd theorem for perfect weighted coverings
Perfect weighted coverings with radius one
Weighted coverings and nonexistence results
Multiple Coverings
Definitions
Perfect multiple coverings
Normality of multiple coverings
Tables for multiple coverings
Multiple coverings of deep holes
Football Pools
Constructions for mixed binary/ternary codes
Tables for mixed binary/ternary codes
on the early history of the ternary Golay code
Tilings
Preliminaries
A sufficient condition
Small tiles
Periodicity of tilings
Recursive decomposition of tilings
Tilings and perfect binary codes
Nonexistence results
Writing on Constrained Memories
Worst case coverings and WOMs
The error case
A model for correcting single errors
Single-error-correcting WOM-codes
Nonlinear WOM-codes
Subset Sums and Constrained Memories
Cayley graphs
Subset sums
Maximal sum-free sets
Constrained memories (W*Ms)
Translation-invariant constraints
Domatic number and reluctant memories
Defective memories
Heterodox Coverings
Perfect coverings by L-spheres
Perfect coverings by spheres of two radii
Coverings by spheres all of different radii
Multicovering radius
Perfect coverings of a sphere and constant weight coverings
Complexity
Introduction
Covering problems
Applications
3.

図書
図書
3. Sphere packings, lattices and groups. 2nd ed (: us ; : gw)
J.H. Conway, N.J.A. Sloane ; with additional contributions by E. Bannai ... [et al.]
出版情報: New York : Springer-Verlag, c1993  xliii, 679 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 290
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4.

図書
図書
4. Finite packing and covering (: hardback)
Károly Böröczky, Jr
出版情報: Cambridge, U.K. : Cambridge University Press, 2004  xvii, 380 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 154
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5.

図書
図書
5. Random sequential packing of cubes
Mathieu Dutour Sikirić, Yoshiaki Itoh
出版情報: New Jersey : World Scientific, c2011  xiii, 240 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / 1：
The Flory model / 2：
One-dimensional discrete random sequential packing / 2.1：
Application of generating function / 2.2：
Number of gaps / 2.3：
Minimum of gaps / 2.4：
Packing on circle and numerical study / 2.5：
Appendix: Complex Analysis / 2.6：
Random interval packing / 3：
The probabilistic setup of the problem / 3.1：
The solution of the delay differential equation using Laplace transform / 3.2：
The computation of the limit / 3.3：
Packing on circle and the speed of convergence / 3.4：
Appendix: The Laplace transform / 3.5：
On the minimum of gaps generated by 1-dimensional random packing / 4：
Main properties of Pr(L(x) ? h) / 4.1：
Laplace transform of Pr(L(x) ? h) / 4.2：
Numerical calculations for a (h) / 4.3：
Asymptotic analysis for a(h) / 4.4：
Renewal equation technique / 4.4.1：
Approximation for small 1 - h / 4.4.2：
Approximation for small h / 4.4.3：
Maximum of gaps / 4.5：
Appendix: Renewal equations / 4.6：
Integral equation method for the 1-dimensional random packing / 5：
The variance and the central limit theorem / 5.1：
Random sequential bisection and its associated binary tree / 6：
Random sequential bisection / 6.1：
Binary search tree / 6.2：
Expected number of nodes at the d-th level / 6.3：
Exponential distribution and uniform distribution / 6.4：
Asymptotic size of the associated tree / 6.5：
Asymptotic shape of the associated tree / 6.6：
More on the associated tree / 6.7：
The unified Kakutani Rényi model / 7：
The limit random packing density / 7.1：
Expectation and variance of number of cars for l = 0 / 7.2：
The central limit theorem / 7.3：
Almost sure convergence results / 7.4：
The limit distribution of a randomly chosen gap / 7.5：
Parking cars with spin but no length / 8：
Integral equations / 8.1：
Existence of the limit packing density / 8.2：
Laplace transform and explicitly solvable cases / 8.3：
General solution methods / 8.4：
The power series solution / 8.5：
Numerical computations / 8.6：
Random sequential packing simulations / 9：
Sequential random packing and the covering problem / 9.1：
Random packing of spheres / 9.2：
Random packing of cubes / 9.3：
Random sequential coding by Hamming distance / 9.4：
Frequency of getting Golay code by a random sequential packing / 9.5：
Discrete cube packings in the cube / 10：
Setting of a goal / 10.1：
Reduction to another problem / 10.2：
Proof of the theorem / 10.3：
Discrete cube packings in the torus / 11：
Algorithm for generating cube packings / 11.1：
Non-extensible cube packings / 11.3：
The second moment / 11.4：
Appendix: Crystallographic groups / 11.5：
Continuous random cube packings in cube and torus / 12：
Combinatorial cube packings / 12.1：
Discrete random cube packings of the cube / 12.3：
Combinatorial torus cube packings and lamination construction / 12.4：
Properties of non-extensible cube packings / 12.5：
Combinatorial Enumeration / Appendix A：
The isomorphism and automorphism problems / A.l：
Sequential exhaustive enumeration / A.2：
The homomorphism principle / A.3：
Bibliography
Index
Preface
Introduction / 1：
The Flory model / 2：
6.

図書
図書
6. Sphere packings, lattices and groups (: U.S ; : Germany)
J.H. Conway, N.J.A. Sloane, with additional contributions by E. Bannai ... [et al.]
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xxvii, 663 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 290
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