Quaternary Codes - Wan, Zhe-Xian

Quaternary Codes

Zhe-Xian Wan

Yayınevi: World Scientific

Yayın tarihi: 01/1998

ISBN: 9789810232740

Ciltli | İngilizce | 242 Sayfa | 15,49 cm x 21,84 cm

Tür: Matematik-İstatistik

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In recent years, quaternary codes have attracted the attention of the coding comminity as several notorious binary nonlinear codes containing more codewords than any known linear codes were found to be binary images under the Gray map of linear codes over Z4. This discovery opens the way for a broader study of quaternary codes, which constitute a rapidly growing area of coding theory. Based on the author's lectures, the book covers the most recent developments in the theory.

Contents:
1 Quaternary Linear Codes and Their Generator Matrices
2 Weight Enumerators
3 The Gray Map
4 Z[subscript 4]-Linearity and Z[subscript 4]-Nonlinearity of Some Binary Linear Codes
5 Hensel's Lemma and Hensel Lift
6 Galois Rings
7 Cyclic Codes
8 Kerdock Codes
9 Preparata Codes
10 Generalizations of Quaternary Kerdock and Preparata Codes
11 Quaternary Quadratic Residue Codes
12 Quaternary Codes and Lattices
13 Some Invariant Theory
14 Self-dual Quaternary Codes and Their Weight Enumerators

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