MinT - Information on Result #942044

Information on Result #942044

Linear OOA(4²⁰³, 103, F₄, 2, 172) (dual of [(103, 2), 3, 173]-NRT-code), using juxtaposition based on

linear OOA(4⁷, 5, F₄, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,4) [i]
linear OOA(4¹⁹³, 98, F₄, 2, 164) (dual of [(98, 2), 3, 165]-NRT-code), using
- strength reduction [i] based on linear OOA(4¹⁹³, 98, F₄, 2, 165) (dual of [(98, 2), 3, 166]-NRT-code), using
  - juxtaposition [i] based on
    1. 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]
    2. linear OOA(4¹⁷⁵, 89, F₄, 2, 150) (dual of [(89, 2), 3, 151]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(4⁷, 5, F₄, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code) (see above)
        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(4²⁰³, 103, F₄, 2, 171) (dual of [(103, 2), 3, 172]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²¹³, 108, F₄, 2, 180) (dual of [(108, 2), 3, 181]-NRT-code)	[i]		Juxtaposition for OOAs