MinT - Information on Result #1086538

Information on Result #1086538

Linear OOA(2²¹¹, 57, F₂, 4, 126) (dual of [(57, 4), 17, 127]-NRT-code), using juxtaposition based on

linear OOA(2⁵¹, 17, F₂, 4, 36) (dual of [(17, 4), 17, 37]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,31P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴³, 40, F₂, 4, 89) (dual of [(40, 4), 17, 90]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁴³, 41, F₂, 4, 89) (dual of [(41, 4), 21, 90]-NRT-code), using
  - algebraic-geometric NRT-code AG(4;F,74P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, 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(2²¹¹, 57, F₂, 4, 125) (dual of [(57, 4), 17, 126]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²¹¹, 57, F₂, 4, 124) (dual of [(57, 4), 17, 125]-NRT-code)	[i]		Strength Reduction for OOAs