| Refereed Publications
- T. Kohnosu, K. Tokiwa, and T. Nishijima, Convergent
Points of Asymptotic Distance Ratio of Some Justesen Codes,
IEICE Transactions on Fundamentals of Electronics, Communications
and Computer Science, Vol. J91A No.5, pp. 587-590, May
Abstract - By using
a feature structure of the Justesen code, the weight distributions
for the families of the Justesen codes having low code
rates are explicitly given by Kolev and Kohnosu--Tokiwa.
However, an asymptotic evaluation to these families is
not given in those papers. Then, the convergent points
of the asymptotic distance ratio that those families have
are specified on the basis of not a lower bound but minimum
weights obtained from those weight distributions. Comparing
with the lower bound on the asymptotic distance ratio
for Justesen codes, the location of the asymptotic ability
that those families have is clarified in this report.
- T. Nishijima, An Upper and a Lower Bound on the
Probability of an Undetected Error for Binary Expansions
of Generalized Reed-Solomon Codes, IEICE Transactions
on Fundamentals of Electronics, Communications and Computer
Science, Vol. J91A No.6, pp. 676-684, June 2008.
Abstract - By utilizing
certain characteristic structure of the Hamming weight
distribution of maximum distance separable codes, we can
get weight enumerators to compute an upper and a lower
bound on the probability of an undetected error for binary
expansions of generalized Reed-Solomon (GRS) codes. Also,
values of the average probability of an undetected error
are computed by using the average weight distribution
for an ensemble of binary expansions of all codewords
of all GRS codes for some given concrete code parameters.
By comparing these values with values of the upper and
the lower bound computed by using the proposed weight
enumerators, the effectiveness of those weight enumerators
is shown in this paper.
- T. Nishijima, K. Tokiwa, and T. Kohnosu, Some
Properties of the Binary Weight Enumerators for Randomly
Shifted Codes and Wozencraft's Ensemble, Technical
Report of IEICE, IT2008-35, pp. 91-94, Sept. 2008.
- T. Endo, T. Nishijima, K. Tokiwa, and T. Kohnosu, Classification
of the Binary Weight Enumerator of Primitive Reed-Solomon
Codes, Technical Report of IEICE, IT2008-36, pp.
95-98, Sept. 2008.
- T. Nishijima, K. Tokiwa, and T. Kohnosu, Specifying
Primitive Reed-Solomon Codes in the Ensemble of Generalized
Reed-Solomon Codes, in Proceedings of the 2008 Symposium
on Information Theory and Its Applications, pp. 724-726,