Abstract
Since their definition in 1984 [7] there has been much work on duadic codes with generalizations in various directions. We survey this for its own interest and as it might shed light on cyclic codes in general. Duadic codes are generalizations of quadratic residue codes. This tells us for which lengths n they exist and also gives us an easy way to construct their generating idempotents over fields of characteristic 2. As cyclic codes whose extensions are self-dual must be duadic, we also learn at which lengths such codes can exist. On the one hand duadic codes are generalized to triadic and polyadic codes, and on the other hand to codes generated by difference sets in abelian groups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. A. Brualdi and V. Pless, “Polyadic Codes,” Discrete Applied Math., 25 (1989), 3–17.
W. C. Huffman, V. Job, and V. Pless, “Multipliers and Generalized Multipliers of Cyclic Objects and Cyclic Codes,” J. Comb. Theory A, 63(1993).
N. Ito, “A Characterization of Quadratic Residue Codes,” Mathematical Journal of Okayama University, 28 (1986), 1–5.
N. Ito, “On Cyclic even tournaments,” preprint.
N. Ito, “On Hadamard Tournaments,” Journal of Algebra, 2 (1990), 432–443.
V. Job, “M-adic Residue Codes,” IEEE Trans. Inform. Theory, IT-38(1992), 496–501.
J. S. Leon, J. M. Masley, V. Pless, “Duadic Codes,” IEEE Trans. Inform. Theory,IT-30(1984), 709–714.
J. Nemoyer, Ph.D. Thesis, University of Illinois at Chicago, 1993.
V. Pless, “Introduction to the Theory of Error-Correcting Codes,” second edition, John Wiley and Sons, New York, 1989.
V. Pless, “Q-Codes,” J.Comb. Theory A, 43 (1986), 258–276.
V. Pless, “Cyclic Projective Planes and Binary, Extended Cyclic Self-Dual Codes,” J. Comb. Theory A, 43 (1986), 331–333.
V. Pless, “Duadic Codes Revisited,” Congressus Numerantiwn, 59 (1987), 225–233.
V. Pless, J. M. Masley, and J. S. Leon, “On Weights in Duadic Codes,” J. Comb. Theory, 44 (1987), 6–21.
V. Pless, J. J. Rushanan, “Triadic Codes,” Linear Algebra Appl., 98 (1988), 415–433.
J. J. Rushanan, “Generalized Q-Codes,” Ph.D. Thesis, Caltech., 1986.
J. J. Rushanan, “Duadic Codes and Difference Sets,” J. Comb. Theory, 57 (1991), 254–261.
M. H. M. Smid, “Duadic Codes,” IEEE Trans. Inform. Theory,IT-33(1987), 432–433.
H. C. A. van Tilborg, “On weights in codes,” Department of Mathematics, Tech. Univ. of Eindhoven, #71, The Netherlands, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Wien
About this chapter
Cite this chapter
Pless, V. (1993). Duadic Codes and Generalizations. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2786-5_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
Online ISBN: 978-3-7091-2786-5
eBook Packages: Springer Book Archive