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The Lower Bound of Constant Dimension Codes in Finite Fields
Pages: 100-105
Year: Issue:  7
Journal: Mathematics in Practice and Theory

Keyword:  constant dimension codeslower bounddual space;
Abstract: Constant-dimension codes become interesting because of their significance to error control in noncoherent random linear network coding.However,the maximal cardinality of any constant dimension code with finite dimension and minimum distance remains unknown.Tuvi Etzion and Alexander Vardy presented the lower bound and the upper bound for a constant dimension code.In this paper,using dual space we first construct a constant dimension code C(n,M,2k,k) that reaches the lower bound,and then construct an optimal constant dimension code C(7,41,4,2).
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