MinT - Information on Result #894660

Information on Result #894660

Linear OOA(2¹¹², 60, F₂, 2, 58) (dual of [(60, 2), 8, 59]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵³, 30, F₂, 2, 29) (dual of [(30, 2), 7, 30]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁴, 15, F₂, 2, 14) (dual of [(15, 2), 6, 15]-NRT-code), using
    - strength reduction [i] based on linear OOA(2²⁴, 15, F₂, 2, 15) (dual of [(15, 2), 6, 16]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(8³, 5, F₈, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,8) or 5-cap in PG(2,8)), using
        discarding factors / shortening the dual code based on linear OA(8³, 8, F₈, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
        Reedâ€“Solomon code RS(5,8) [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]
  2. linear OOA(2²⁹, 15, F₂, 2, 29) (dual of [(15, 2), 1, 30]-NRT-code), using
    - dual of repetition NRT-code with length 15 [i]
linear OOA(2⁵⁹, 30, F₂, 2, 58) (dual of [(30, 2), 1, 59]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁵⁹, 30, F₂, 2, 59) (dual of [(30, 2), 1, 60]-NRT-code), using
  - dual of repetition NRT-code with length 30 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³¹, 120, F₂, 2, 116) (dual of [(120, 2), 9, 117]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²³¹, 120, F₂, 2, 117) (dual of [(120, 2), 9, 118]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs