MinT - Information on Result #1143509

Information on Result #1143509

Linear OOA(2¹⁸⁶, 1430866, F₂, 6, 13) (dual of [(1430866, 6), 8585010, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁷, 32766, F₂, 6, 6) (dual of [(32766, 6), 196549, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁴⁷, 32767, F₂, 3, 6) (dual of [(32767, 3), 98254, 7]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁴⁷, 32767, F₂, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹³⁹, 1398100, F₂, 6, 13) (dual of [(1398100, 6), 8388461, 14]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁸⁶, 1430866, F₂, 6, 12) (dual of [(1430866, 6), 8585010, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁵⁰, 2861732, F₂, 6, 13) (dual of [(2861732, 6), 17170142, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2¹⁸⁶, 1430865, F₂, 7, 13) (dual of [(1430865, 7), 10015869, 14]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(2¹⁸⁶, 1430865, F₂, 8, 13) (dual of [(1430865, 8), 11446734, 14]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁶, 1430865, F₂, 18, 13) (dual of [(1430865, 18), 25755384, 14]-NRT-code)	[i]