MinT - Information on Result #894665

Information on Result #894665

Linear OOA(2¹¹⁶, 62, F₂, 2, 60) (dual of [(62, 2), 8, 61]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁵, 31, F₂, 2, 30) (dual of [(31, 2), 7, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁵⁵, 32, F₂, 2, 30) (dual of [(32, 2), 9, 31]-NRT-code), using
  - 2 times NRT-code embedding in larger space [i] based on linear OOA(2⁵¹, 30, F₂, 2, 30) (dual of [(30, 2), 9, 31]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁵¹, 30, F₂, 2, 31) (dual of [(30, 2), 9, 32]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
        Denniston code D(1,8) [i]
        linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
linear OOA(2⁶¹, 31, F₂, 2, 60) (dual of [(31, 2), 1, 61]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁶¹, 31, F₂, 2, 61) (dual of [(31, 2), 1, 62]-NRT-code), using
  - dual of repetition NRT-code with length 31 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁹, 124, F₂, 2, 120) (dual of [(124, 2), 9, 121]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²³⁹, 124, F₂, 2, 121) (dual of [(124, 2), 9, 122]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs