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Distance-Regular Graphs
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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.Abstract:
Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distanceread more
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The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
TL;DR: 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).
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The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes
TL;DR: 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.
Journal ArticleDOI
Coding for Errors and Erasures in Random Network Coding
TL;DR: A Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.
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Grassmannian frames with applications to coding and communication
Thomas Strohmer,Robert W. Heath +1 more
TL;DR: The application of Grassmannian frames to wireless communication and to multiple description coding is discussed and their connection to unit norm tight frames for frames which are generated by group-like unitary systems is discussed.
Codes and Decoding on General Graphs
TL;DR: It is showed that many iterative decoding algorithms are special cases of two generic algorithms, the min-sum and sum-product algorithms, which also include non-iterative algorithms such as Viterbi decoding.
References
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Symmetric Conference Matrices of Order pq 2 + 1
TL;DR: A conference matrix of order n is a square matrix C with zeros on the diagonal and ± 1 elsewhere, which satisfies the orthogonality condition CCT = (n − 1)I as mentioned in this paper.