MinT - Information on Result #1025549

Information on Result #1025549

Linear OOA(2⁸⁶, 31, F₂, 3, 54) (dual of [(31, 3), 7, 55]-NRT-code), using juxtaposition based on

linear OOA(2²⁰, 9, F₂, 3, 15) (dual of [(9, 3), 7, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;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]
linear OOA(2⁵⁹, 22, F₂, 3, 38) (dual of [(22, 3), 7, 39]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁷, 8, F₂, 3, 13) (dual of [(8, 3), 7, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;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]
  2. linear OOA(2³⁵, 14, F₂, 3, 24) (dual of [(14, 3), 7, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,17P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, 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(2⁸⁶, 31, F₂, 3, 53) (dual of [(31, 3), 7, 54]-NRT-code)	[i]		Strength Reduction for OOAs