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In recent years quaternary codes have attracted the attention of the coding community 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 94. This discovery opens the way for a broader study of quaternary codes, which constitute a rapidly growing area of coding theory. This book is based on the author's lectures in Xi'an, China and Lund, Sweden and covers the most recent developments of this theory.
Contents:
- Quaternary Linear Codes and Their Generator Matrices
- Weight Enumerators
- The Gray Map
- 94-Linearity and (94-Nonlinearity of Some Binary Linear Codes
- Hensel's Lemma and Hensel Lift
- Galois Rings
- Cyclic Codes
- Kerdock Codes
- Preparata Codes
- Generalizations of Quaternary Kerdock and Preparata Codes
- Quaternary Quadratic Residue Codes
- Quaternary Codes and Lattices
- Some Invariant Theory
- Self-Dual Quaternary Codes and Their Weight Enumerators
Readership: Applied mathematicians.
