MinT - Information on Result #941988

Information on Result #941988

Linear OOA(4²¹⁰, 107, F₄, 2, 174) (dual of [(107, 2), 4, 175]-NRT-code), using juxtaposition based on

linear OOA(4¹⁰, 7, F₄, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁰, 9, F₄, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4¹⁹⁶, 100, F₄, 2, 164) (dual of [(100, 2), 4, 165]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4⁶, 5, F₄, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;4,4) [i]
  2. linear OOA(4¹⁸⁶, 95, F₄, 2, 157) (dual of [(95, 2), 4, 158]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4⁶, 5, F₄, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code) (see above)
      2. linear OOA(4¹⁷⁶, 90, F₄, 2, 150) (dual of [(90, 2), 4, 151]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(4⁶, 5, F₄, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code) (see above)
        linear OOA(4¹⁶⁶, 85, F₄, 2, 143) (dual of [(85, 2), 4, 144]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(16¹⁵, 17, F₁₆, 15) (dual of [17, 2, 16]-code or 17-arc in PG(14,16)), using
        extended Reedâ€“Solomon code RS_e(2,16) [i]
        Simplex code S(2,16) [i]
        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		Method
1	Linear OOA(4²¹⁰, 107, F₄, 2, 173) (dual of [(107, 2), 4, 174]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²¹⁰, 107, F₄, 2, 172) (dual of [(107, 2), 4, 173]-NRT-code)	[i]
3	Linear OOA(4²¹⁰, 107, F₄, 2, 171) (dual of [(107, 2), 4, 172]-NRT-code)	[i]
4	Linear OOA(4²¹⁰, 107, F₄, 2, 170) (dual of [(107, 2), 4, 171]-NRT-code)	[i]
5	Linear OOA(4²¹⁰, 107, F₄, 2, 169) (dual of [(107, 2), 4, 170]-NRT-code)	[i]
6	Linear OOA(4²¹⁰, 107, F₄, 2, 168) (dual of [(107, 2), 4, 169]-NRT-code)	[i]