MinT - Information on Result #2442173

Information on Result #2442173

Linear OOA(4¹⁸⁸, 97, F₄, 2, 149) (dual of [(97, 2), 6, 150]-NRT-code), using strength reduction based on linear OOA(4¹⁸⁸, 97, F₄, 2, 151) (dual of [(97, 2), 6, 152]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁸, 7, F₄, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁸, 9, F₄, 2, 7) (dual of [(9, 2), 10, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [i]
2. linear OOA(4¹⁷⁴, 90, F₄, 2, 143) (dual of [(90, 2), 6, 144]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹⁵, 18, F₁₆, 15) (dual of [18, 3, 16]-code or 18-arc in PG(14,16)), using
      - Denniston code D(1,16) [i]
    2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [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(4¹⁹⁶, 100, F₄, 2, 154) (dual of [(100, 2), 4, 155]-NRT-code)	[i]		Juxtaposition for OOAs