| 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 | |
| Constructions | |
| 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 | |
| The error case | |
| 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 | |
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