MinT - Information on Result #1029405

Information on Result #1029405

Linear OOA(2¹⁵¹, 69, F₂, 3, 63) (dual of [(69, 3), 56, 64]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(4⁴¹, 23, F₄, 3, 31) (dual of [(23, 3), 28, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴¹, 26, F₄, 3, 31) (dual of [(26, 3), 37, 32]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,46P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]
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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁵¹, 69, F₂, 3, 62) (dual of [(69, 3), 56, 63]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁵¹, 69, F₂, 3, 61) (dual of [(69, 3), 56, 62]-NRT-code)	[i]		Strength Reduction for OOAs