MinT - Information on Result #1653055

Information on Result #1653055

Linear OOA(256⁵⁰, 530, F₂₅₆, 5, 32) (dual of [(530, 5), 2600, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵⁰, 530, F₂₅₆, 4, 32) (dual of [(530, 4), 2070, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵⁰, 578, F₂₅₆, 4, 32) (dual of [(578, 4), 2262, 33]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹⁷, 289, F₂₅₆, 4, 16) (dual of [(289, 4), 1139, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,1139P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(256³³, 289, F₂₅₆, 4, 32) (dual of [(289, 4), 1123, 33]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,1123P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289 (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.