Open AccessPosted Content
The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes
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TLDR
In this paper, it was shown that all the nonlinear binary codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals can be constructed as binary images under the Gray map of linear codes over Z_4, the integers mod 4.Citations
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Journal ArticleDOI
Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes
James A. Davis,Jonathan Jedwab +1 more
TL;DR: A previously unrecognized connection between Golay complementary sequences and second-order Reed-Muller codes over alphabets Z/sub 2/h is found to give an efficient decoding algorithm involving multiple fast Hadamard transforms.
Book ChapterDOI
Boolean Models and Methods in Mathematics, Computer Science, and Engineering: Boolean Functions for Cryptography and Error-Correcting Codes
TL;DR: Encryption-decryption is the most ancient cryptographic activity, but its nature has deeply changed with the invention of computers, because the cryptanalysis (the activity of the third person, the eavesdropper, who aims at recovering the message) can use their power.
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Packing Lines, Planes, etc.: Packings in Grassmannian Space
TL;DR: 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.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
Error control coding : fundamentals and applications
Shu Lin,Daniel J. Costello +1 more
TL;DR: This book explains coding for Reliable Digital Transmission and Storage using Trellis-Based Soft-Decision Decoding Algorithms for Linear Block Codes and Convolutional Codes, and some of the techniques used in this work.
Book
Distance-Regular Graphs
TL;DR: In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.