论文信息 - Linear Codes with Exponentially Many Light Vectors

Linear Codes with Exponentially Many Light Vectors

G. Kalai and N. Linial (1995, IEEE Trans. Inform. Theory41, 1467?1472) put forward the following conjecture: Let {Cn} be a sequence of binary linear codes of distance dn and Adn be the number of vectors of weight dn in Cn. Then log2Adn=o(n). We disprove this by constructing a family of linear codes from geometric Goppa codes in which the number of vectors of minimum weight grows exponentially with the length.

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