MinT - Information on Result #1049472

Information on Result #1049472

Linear OOA(2¹⁸⁷, 64, F₂, 3, 133) (dual of [(64, 3), 5, 134]-NRT-code), using juxtaposition based on

linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁷², 59, F₂, 3, 123) (dual of [(59, 3), 5, 124]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code) (see above)
  2. linear OOA(2¹⁵⁷, 54, F₂, 3, 113) (dual of [(54, 3), 5, 114]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code) (see above)
      2. linear OOA(2¹⁴², 49, F₂, 3, 103) (dual of [(49, 3), 5, 104]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code) (see above)
        linear OOA(2¹²⁷, 44, F₂, 3, 93) (dual of [(44, 3), 5, 94]-NRT-code), using
        2 step truncation [i] based on linear OOA(2¹²⁹, 45, F₂, 3, 95) (dual of [(45, 3), 6, 96]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
        linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)

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(2¹⁸⁷, 64, F₂, 3, 132) (dual of [(64, 3), 5, 133]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁸⁷, 32, F₂, 6, 133) (dual of [(32, 6), 5, 134]-NRT-code)	[i]		OOA Folding