MinT - Information on Result #1025516

Information on Result #1025516

Linear OOA(2¹⁹¹, 66, F₂, 3, 116) (dual of [(66, 3), 7, 117]-NRT-code), using juxtaposition based on

linear OOA(2¹⁴, 7, F₂, 3, 11) (dual of [(7, 3), 7, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁷⁰, 59, F₂, 3, 104) (dual of [(59, 3), 7, 105]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁷⁰, 60, F₂, 3, 104) (dual of [(60, 3), 10, 105]-NRT-code), using
  - 13 step truncation [i] based on linear OOA(2¹⁸³, 65, F₂, 3, 117) (dual of [(65, 3), 12, 118]-NRT-code), using
    - strength reduction [i] based on linear OOA(2¹⁸³, 65, F₂, 3, 120) (dual of [(65, 3), 12, 121]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹⁰, 13, F₁₆, 10) (dual of [13, 3, 11]-code or 13-arc in PG(9,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
        Reedâ€“Solomon code RS(6,16) [i]
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹², 73, F₂, 3, 128) (dual of [(73, 3), 7, 129]-NRT-code)	[i]		Juxtaposition for OOAs