MinT - Information on Result #909781

Information on Result #909781

Linear OOA(4²⁴⁵, 125, F₄, 2, 187) (dual of [(125, 2), 5, 188]-NRT-code), using juxtaposition based on

linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4²¹⁷, 111, F₄, 2, 166) (dual of [(111, 2), 5, 167]-NRT-code), using
- strength reduction [i] based on linear OOA(4²¹⁷, 111, F₄, 2, 174) (dual of [(111, 2), 5, 175]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4²¹, 13, F₄, 2, 18) (dual of [(13, 2), 5, 19]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4²¹, 14, F₄, 2, 18) (dual of [(14, 2), 7, 19]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
    2. linear OOA(4¹⁹¹, 98, F₄, 2, 155) (dual of [(98, 2), 5, 156]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(4¹⁷³, 89, F₄, 2, 142) (dual of [(89, 2), 5, 143]-NRT-code), using
        1 step truncation [i] based on linear OOA(4¹⁷⁴, 90, F₄, 2, 143) (dual of [(90, 2), 6, 144]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        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]
        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(4²⁴⁵, 125, F₄, 2, 186) (dual of [(125, 2), 5, 187]-NRT-code)	[i]		Strength Reduction for OOAs