MinT - Information on Result #2928831

Information on Result #2928831

Linear OOA(2²⁵⁵, 52, F₂, 6, 172) (dual of [(52, 6), 57, 173]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁵⁴, 52, F₂, 6, 172) (dual of [(52, 6), 58, 173]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁵⁴, 52, F₂, 6, 173) (dual of [(52, 6), 58, 174]-NRT-code), using
- constructionÂ X applied to AG(6;F,57P) âŠ‚ AG(6;F,63P) [i] based on
  1. linear OOA(2²⁴², 48, F₂, 6, 173) (dual of [(48, 6), 46, 174]-NRT-code), using algebraic-geometric NRT-code AG(6;F,57P) 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(2²³⁰, 48, F₂, 6, 161) (dual of [(48, 6), 58, 162]-NRT-code), using algebraic-geometric NRT-code AG(6;F,63P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
  3. linear OOA(2¹², 4, F₂, 6, 11) (dual of [(4, 6), 12, 12]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2¹², 5, F₂, 5, 11) (dual of [(5, 5), 13, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(5;F,13P) [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.