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The Theory of Error-Correcting Codes
Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the Golay Code. An Introduction to BCH Codes and Finite Fields. Finite Fields. Dual Codes and Their Weight Distribution. Codes, DesignsExpand
The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 24 December 2003
TLDR
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used. Expand
Sphere Packings, Lattices and Groups
  • J. Conway, N. Sloane
  • Mathematics, Computer Science
  • Grundlehren der mathematischen Wissenschaften
  • 1 December 1987
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue toExpand
Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959.
TLDR
For a wide class of distortion measures and discrete sources of information there exists a functionR(d) (depending on the particular distortion measure and source) which measures the equivalent rateR of the source (in bits per letter produced) whendis the allowed distortion level. Expand
Quantum Error Correction Via Codes Over GF(4)
TLDR
In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Expand
Quantum error correction via codes over GF(4)
The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. ThisExpand
A new upper bound on the minimal distance of self-dual codes
It is shown that the minimal distance d of a binary self-dual code of length n>or=74 is at most 2((n+6)/10). This bound is a consequence of some new conditions on the weight enumerator of a self-dualExpand
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
TLDR
Certain notorious nonlinear binary codes contain more codewords than any known linear code and can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). Expand
Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
TLDR
A reformulation of the problem gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension ½(m–l)(m+2), which provides a (usually) lowerdimensional representation than the Plucker embedding and leads to a proof that many of the new packings are optimal. Expand
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