MinT - Information on Result #1086922

Information on Result #1086922

Linear OOA(2²⁵⁷, 66, F₂, 4, 182) (dual of [(66, 4), 7, 183]-NRT-code), using juxtaposition based on

linear OOA(2²¹, 7, F₂, 4, 18) (dual of [(7, 4), 7, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,9P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²²⁹, 59, F₂, 4, 163) (dual of [(59, 4), 7, 164]-NRT-code), using
- strength reduction [i] based on linear OOA(2²²⁹, 59, F₂, 4, 164) (dual of [(59, 4), 7, 165]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²⁹, 9, F₂, 4, 24) (dual of [(9, 4), 7, 25]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁹³, 50, F₂, 4, 139) (dual of [(50, 4), 7, 140]-NRT-code), using
      - repeating each code word 5 times [i] based on linear OOA(2³³, 10, F₂, 4, 27) (dual of [(10, 4), 7, 28]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,12P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, 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(2²⁵⁷, 66, F₂, 4, 181) (dual of [(66, 4), 7, 182]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁵⁷, 66, F₂, 4, 180) (dual of [(66, 4), 7, 181]-NRT-code)	[i]		Strength Reduction for OOAs