MinT - Information on Result #941516

Information on Result #941516

Linear OOA(2¹⁰¹, 55, F₂, 2, 56) (dual of [(55, 2), 9, 57]-NRT-code), using juxtaposition based on

linear OOA(2¹¹, 10, F₂, 2, 7) (dual of [(10, 2), 9, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹¹, 11, F₂, 2, 7) (dual of [(11, 2), 11, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (4, 11, 11)-net over F₂, using
    - a shift-net [i]
linear OOA(2⁸¹, 45, F₂, 2, 48) (dual of [(45, 2), 9, 49]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(8⁶, 9, F₈, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,8)), using
    - extended Reedâ€“Solomon code RS_e(3,8) [i]
  2. linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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(2¹⁰¹, 55, F₂, 2, 55) (dual of [(55, 2), 9, 56]-NRT-code)	[i]		Strength Reduction for OOAs