MinT - Information on Result #1462093

Information on Result #1462093

Linear OOA(49²⁶, 126, F₄₉, 2, 16) (dual of [(126, 2), 226, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(49²⁶, 126, F₄₉, 16) (dual of [126, 100, 17]-code), using

discarding factors / shortening the dual code based on linear OA(49²⁶, 128, F₄₉, 16) (dual of [128, 102, 17]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(49⁹, 64, F₄₉, 8) (dual of [64, 55, 9]-code), using
    - extended algebraic-geometric code AG_e(F,55P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OA(49¹⁷, 64, F₄₉, 16) (dual of [64, 47, 17]-code), using
    - extended algebraic-geometric code AG_e(F,47P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64 (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.