MinT - Information on Result #942091

Information on Result #942091

Linear OOA(4¹⁹⁹, 101, F₄, 2, 170) (dual of [(101, 2), 3, 171]-NRT-code), using juxtaposition based on

linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,3P) [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(4¹⁸¹, 92, F₄, 2, 155) (dual of [(92, 2), 3, 156]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹³, 8, F₄, 2, 12) (dual of [(8, 2), 3, 13]-NRT-code), using
    - discarding factors / shortening the dual code 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 (see above)
  2. linear OOA(4¹⁶⁵, 84, F₄, 2, 142) (dual of [(84, 2), 3, 143]-NRT-code), using
    - 1 step truncation [i] based on 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²¹⁷, 110, F₄, 2, 185) (dual of [(110, 2), 3, 186]-NRT-code)	[i]		Juxtaposition for OOAs