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Linear Codes with Exponentially Many Light Vectors

✍ Scribed by Alexei Ashikhmin; Alexander Barg; Serge Vlăduţ

Book ID
102586736
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
76 KB
Volume
96
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

put forward the following conjecture: Let {C n } be a sequence of binary linear codes of distance d n and A dn be the number of vectors of weight d n in C n . Then log 2 A dn =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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