Abstract
In this paper, we look at self-dual codes over the ring Z 16 of integers modulo 16. From any doubly even self-dual binary code, we construct codes over Z 16 and give a necessary and sufficient condition for the self-duality of induced codes. We then give an inductive algorithm for constructing all self-dual codes over Z 16 , and establish the mass formula, which counts the number of such codes.
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References
Balmaceda, J., Betty, R., Nemenzo, F.: Mass formula for self-dual codes over \(Z_{p^2}\). Discrete Mathematics 308, 2984–3002 (2008)
Dougherty, S., Harada, M., Solé, P.: Self-dual codes over rings and the Chinese remainder theorem. Hokkaido Math. J. 28, 253–283 (1999)
Fields, J., Gaborit, P., Leon, J., Pless, V.: All self-dual Z 4 codes of length 15 or less are known. IEEE Trans. Inform. Theory 44, 311–322 (1998)
Gaborit, P.: Mass formulas for self-dual codes over Z 4 and \({\mathbb F}_q+u{\mathbb F}_q\) rings. IEEE Trans. Inform. Theory 42, 1222–1228 (1996)
Hammons, A., Kumar, P., Calderbank, A., Sloane, N., Solé, P.: The Z 4 linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inform. Theory 40, 301–319 (1994)
Nagata, K., Nemenzo, F., Wada, H.: The number of self-dual codes over \(Z_{p^3}\). Designs, Codes and Cryptography 50, 291–303 (2009)
Nagata, K., Nemenzo, F., Wada, H.: Constructive algorithm of self-dual error-correcting codes. In: Proc. of 11th International Workshop on Algebraic and Combinatorial Coding Theory, pp. 215–220 (2008) ISSN 1313-423X
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Nagata, K., Nemenzo, F., Wada, H. (2009). On Self-dual Codes over Z 16 . In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_12
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DOI: https://doi.org/10.1007/978-3-642-02181-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02180-0
Online ISBN: 978-3-642-02181-7
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