MinT - Information on Result #941642

Information on Result #941642

Linear OOA(2⁹⁰, 47, F₂, 2, 60) (dual of [(47, 2), 4, 61]-NRT-code), using juxtaposition based on

linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;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]
linear OOA(2⁸⁰, 42, F₂, 2, 54) (dual of [(42, 2), 4, 55]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(4¹², 14, F₄, 10) (dual of [14, 2, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹², 16, F₄, 10) (dual of [16, 4, 11]-code), using
      - 1 times truncation [i] based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
  2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁸⁸, 46, F₂, 2, 58) (dual of [(46, 2), 4, 59]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(2¹⁰⁰, 52, F₂, 2, 66) (dual of [(52, 2), 4, 67]-NRT-code)	[i]		Juxtaposition for OOAs