MinT - Information on Result #2846921

Information on Result #2846921

Linear OOA(2²³⁷, 79, F₂, 5, 87) (dual of [(79, 5), 158, 88]-NRT-code), using strength reduction based on linear OOA(2²³⁷, 79, F₂, 5, 88) (dual of [(79, 5), 158, 89]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁹⁰, 35, F₂, 5, 44) (dual of [(35, 5), 85, 45]-NRT-code), using
  - constructionÂ X applied to AG(5;F,115P) âŠ‚ AG(5;F,123P) [i] based on
    1. linear OOA(2⁸³, 32, F₂, 5, 44) (dual of [(32, 5), 77, 45]-NRT-code), using algebraic-geometric NRT-code AG(5;F,115P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(2⁷⁵, 32, F₂, 5, 36) (dual of [(32, 5), 85, 37]-NRT-code), using algebraic-geometric NRT-code AG(5;F,123P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (see above)
    3. linear OOA(2⁷, 3, F₂, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;8,2) [i]
2. linear OOA(2¹⁴⁷, 44, F₂, 5, 88) (dual of [(44, 5), 73, 89]-NRT-code), using
  - constructionÂ X applied to AG(5;F,20P) âŠ‚ AG(5;F,21P) [i] based on
    1. linear OOA(2¹⁴³, 42, F₂, 5, 89) (dual of [(42, 5), 67, 90]-NRT-code), using algebraic-geometric NRT-code AG(5;F,20P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹³⁷, 42, F₂, 5, 83) (dual of [(42, 5), 73, 84]-NRT-code), using algebraic-geometric NRT-code AG(5;F,21P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
    3. linear OOA(2⁴, 2, F₂, 5, 4) (dual of [(2, 5), 6, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(5;6,2) [i]

Mode: Constructive and 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.