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Self-dual codes of lengths less than 5 over ${\mathbb Z}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. {\bf 17} (2011), 442-460]. The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb Z}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small $p$'s are also given.
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참고문헌 (11)
참고문헌 신청
E. Rains / 1998 / the Handbook of Coding Theory / Elsevier
F.J. MacWilliams / 1977 / The theory of error-correcting codes / North-Holland
G. Nebe / 2006 / Self-dual codes and invariant theory / Springer-Verlag
J.H. Conway / 1993 / Self-dual codes over the integers modulo 4 / J. Comin. Theory Ser A 62 : 30 ~ 45
J.M.P. Balmaceda / 2009 / Mass formula for self-dual codes over Zp2 / Discrete Math 308 : 2984 ~ 3002
F.J. MacWilliams / 1977 / The theory of error-correcting codes / North-Holland
G. Nebe / 2006 / Self-dual codes and invariant theory / Springer-Verlag
J.H. Conway / 1993 / Self-dual codes over the integers modulo 4 / J. Comin. Theory Ser A 62 : 30 ~ 45
J.M.P. Balmaceda / 2009 / Mass formula for self-dual codes over Zp2 / Discrete Math 308 : 2984 ~ 3002
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