MinT - Information on Result #2908572

Information on Result #2908572

Linear OOA(2¹⁴³, 46, F₂, 6, 76) (dual of [(46, 6), 133, 77]-NRT-code), using strength reduction based on linear OOA(2¹⁴³, 46, F₂, 6, 77) (dual of [(46, 6), 133, 78]-NRT-code), using

constructionÂ X applied to AG(6;F,29P) âŠ‚ AG(6;F,31P) [i] based on
1. linear OOA(2¹³¹, 42, F₂, 6, 77) (dual of [(42, 6), 121, 78]-NRT-code), using algebraic-geometric NRT-code AG(6;F,29P) 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(2¹¹⁹, 42, F₂, 6, 65) (dual of [(42, 6), 133, 66]-NRT-code), using algebraic-geometric NRT-code AG(6;F,31P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁴⁴, 46, F₂, 6, 76) (dual of [(46, 6), 132, 77]-NRT-code)	[i]		OOA Duplication