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Distance properties of expander codes. (English) Zbl 1282.94107
The authors study the minimum distance of some families of expander codes and also some related families of codes defined on bipartite graphs. They compute the weight spectrum and the minimum distance of a random ensemble of such codes and show that it sometimes meets the Gilbert-Varshamov (GV) bound. A lower bound on the minimum distances of constructive families of expander codes is also derived. They show that relative minimum distance of the expander code exceeds the product bound $$\delta_0\delta_1$$ where $$\delta_0$$ and $$\delta_1$$ are the minimum relative distances of the constituent codes. As a result they obtain a polynomially constructible family of expander codes with relative distance exceeding the Zyablov bound on the distance of serial concatenations.

##### MSC:
 94B65 Bounds on codes 94B25 Combinatorial codes
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