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<p><b>Abstract</b>—An efficient algorithm to count the cardinalities of certain subsets of constant weight binary vectors is presented in this paper. The algorithm enables us to design 1-symmetric error correcting/all unidirectional error detecting (1-syEC/AUED) codes with the highest cardinality based on the group <it>Z</it><sub><it>n</it></sub>. Since a field <it>Z</it><sub><it>p</it></sub> is a group, this algorithm can also be used to design a <it>field</it> 1-syEC/AUED code. We can construct <it>t</it>-syEC/AUED codes for <it>t</it> = 2 or 3 by appending a tail to the <it>field</it> 1-syEC/AUED codes. The information rates of the proposed <it>t</it>-syEC/AUED codes are shown to be better than the previously developed codes.</p>
Balanced codes, error correction, error detection, unidirectional errors, combinatorics, partition problems.

C. Laih and C. Yang, "On the Analysis and Design of Group Theoretical t-syEC/AUED Codes," in IEEE Transactions on Computers, vol. 45, no. , pp. 103-108, 1996.
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