MinT - Information on Result #2443615

Information on Result #2443615

Linear OOA(4²¹³, 109, F₄, 2, 163) (dual of [(109, 2), 5, 164]-NRT-code), using strength reduction based on linear OOA(4²¹³, 109, F₄, 2, 171) (dual of [(109, 2), 5, 172]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4³⁵, 20, F₄, 2, 28) (dual of [(20, 2), 5, 29]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³⁵, 21, F₄, 2, 28) (dual of [(21, 2), 7, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
2. 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
      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(4²²³, 114, F₄, 2, 169) (dual of [(114, 2), 5, 170]-NRT-code)	[i]		Juxtaposition for OOAs