MinT - Information on Result #2928652

Information on Result #2928652

Linear OOA(2²⁴⁷, 61, F₂, 6, 132) (dual of [(61, 6), 119, 133]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁴⁶, 61, F₂, 6, 132) (dual of [(61, 6), 120, 133]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁴⁶, 61, F₂, 6, 133) (dual of [(61, 6), 120, 134]-NRT-code), using
- constructionÂ X applied to AG(6;F,77P) âŠ‚ AG(6;F,94P) [i] based on
  1. linear OOA(2²⁰², 48, F₂, 6, 133) (dual of [(48, 6), 86, 134]-NRT-code), using algebraic-geometric NRT-code AG(6;F,77P) 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(2¹⁶⁸, 48, F₂, 6, 99) (dual of [(48, 6), 120, 100]-NRT-code), using algebraic-geometric NRT-code AG(6;F,94P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
  3. linear OOA(2⁴⁴, 13, F₂, 6, 33) (dual of [(13, 6), 34, 34]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁴⁴, 14, F₂, 6, 33) (dual of [(14, 6), 40, 34]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(6;F,50P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, 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.