MinT - Information on Result #1086933

Information on Result #1086933

Linear OOA(2²⁵³, 65, F₂, 4, 180) (dual of [(65, 4), 7, 181]-NRT-code), using juxtaposition based on

linear OOA(2²⁵, 8, F₂, 4, 21) (dual of [(8, 4), 7, 22]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²²¹, 57, F₂, 4, 158) (dual of [(57, 4), 7, 159]-NRT-code), using
- juxtaposition [i] based on
  1. 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]
  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(2²⁵³, 65, F₂, 4, 179) (dual of [(65, 4), 7, 180]-NRT-code)	[i]		Strength Reduction for OOAs