MinT - Information on Result #1010270

Information on Result #1010270

Linear OOA(2²²¹, 78, F₂, 3, 115) (dual of [(78, 3), 13, 116]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰⁵, 39, F₂, 3, 57) (dual of [(39, 3), 12, 58]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁵, 42, F₂, 3, 57) (dual of [(42, 3), 21, 58]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2¹⁰⁴, 42, F₂, 3, 57) (dual of [(42, 3), 22, 58]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4³¹, 14, F₄, 3, 28) (dual of [(14, 3), 11, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(2¹¹⁶, 39, F₂, 3, 115) (dual of [(39, 3), 1, 116]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁶, 39, F₂, 3, 116) (dual of [(39, 3), 1, 117]-NRT-code), using
  - dual of repetition NRT-code with length 39 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁶⁰, 91, F₂, 3, 131) (dual of [(91, 3), 13, 132]-NRT-code)	[i]		Juxtaposition for OOAs