MinT - Information on Result #1652905

Information on Result #1652905

Linear OOA(256³⁹, 525, F₂₅₆, 5, 25) (dual of [(525, 5), 2586, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256³⁹, 525, F₂₅₆, 4, 25) (dual of [(525, 4), 2061, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256³⁹, 578, F₂₅₆, 4, 25) (dual of [(578, 4), 2273, 26]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹³, 289, F₂₅₆, 4, 12) (dual of [(289, 4), 1143, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,1143P) [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(256²⁶, 289, F₂₅₆, 4, 25) (dual of [(289, 4), 1130, 26]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,1130P) [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.