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RS encoding and decoding for shards #7

@snjax

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@snjax

Represent data as a table with N=2^n rows and M=2^m columns.

Each column corresponds to polynomial coefficients, and each shard corresponds to a point at m31 circle coset with order N*B, where B is the blowup factor.

  • Implement computation of shards rows using columnwise_dot_product (see example )
  • Implement recovery from any N elements from the same coset (N-ordered, there are B such cosets)
  • Implement recovery from any arbitrary N elements, using an inefficient O(N^2) algorithm

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