MinT - Information on Result #2872267

Information on Result #2872267

Linear OOA(2²²³, 52, F₂, 5, 142) (dual of [(52, 5), 37, 143]-NRT-code), using 2¹ times duplication based on linear OOA(2²²², 52, F₂, 5, 142) (dual of [(52, 5), 38, 143]-NRT-code), using

strength reduction [i] based on linear OOA(2²²², 52, F₂, 5, 143) (dual of [(52, 5), 38, 144]-NRT-code), using
- constructionÂ X applied to AG(5;F,48P) âŠ‚ AG(5;F,53P) [i] based on
  1. linear OOA(2²¹², 48, F₂, 5, 143) (dual of [(48, 5), 28, 144]-NRT-code), using algebraic-geometric NRT-code AG(5;F,48P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
  2. linear OOA(2²⁰², 48, F₂, 5, 133) (dual of [(48, 5), 38, 134]-NRT-code), using algebraic-geometric NRT-code AG(5;F,53P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
  3. linear OOA(2¹⁰, 4, F₂, 5, 9) (dual of [(4, 5), 10, 10]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [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.