MinT - Information on Result #894637

Information on Result #894637

Linear OOA(2⁹³, 50, F₂, 2, 49) (dual of [(50, 2), 7, 50]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁴, 25, F₂, 2, 24) (dual of [(25, 2), 6, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁴⁴, 27, F₂, 2, 24) (dual of [(27, 2), 10, 25]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁴⁴, 27, F₂, 2, 25) (dual of [(27, 2), 10, 26]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. 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, using
        the Hermitian function field over F₄ [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(2⁴⁹, 25, F₂, 2, 49) (dual of [(25, 2), 1, 50]-NRT-code), using
- dual of repetition NRT-code with length 25 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁹², 100, F₂, 2, 98) (dual of [(100, 2), 8, 99]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁹², 100, F₂, 2, 99) (dual of [(100, 2), 8, 100]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs