Undetected error probability of q-ary constant weight codes |
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| Authors: | Shu-Tao Xia Fang-Wei Fu |
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| Institution: | (1) The Graduate School at Shenzhen, Tsinghua University, Shenzhen Guangdong, 518055, P.R. China;(2) National Mobile Communications Research Laboratory, Southeast University, Nanjing Jiangsu, P.R. China;(3) Chern Institute of Mathematics and KLPMC, Nankai University, Tianjin, 300071, P.R. China |
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| Abstract: | In this paper, we introduce a new combinatorial invariant called q-binomial moment for q-ary constant weight codes. We derive a lower bound on the q-binomial moments and introduce a new combinatorial structure called generalized (s, t)-designs which could achieve the lower bounds. Moreover, we employ the q-binomial moments to study the undetected error probability of q-ary constant weight codes. A lower bound on the undetected error probability for q-ary constant weight codes is obtained. This lower bound extends and unifies the related results of Abdel-Ghaffar for q-ary codes and Xia-Fu-Ling for binary constant weight codes. Finally, some q-ary constant weight codes which achieve the lower bounds are found.
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| Keywords: | Codes Constant weight codes Distance distribution Error detection Undetected error probability Generalized t-design |
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