MinT - Information on Result #1159814

Information on Result #1159814

Linear OOA(2²⁴⁸, 2396870, F₂, 7, 15) (dual of [(2396870, 7), 16777842, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁸³, 1198435, F₂, 7, 15) (dual of [(1198435, 7), 8388862, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 64, F₂, 7, 7) (dual of [(64, 7), 427, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(2²¹, 64, F₂, 6, 7) (dual of [(64, 6), 363, 8]-NRT-code), using
      - extracting embedded OOA [i] based on digital (14, 21, 64)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶², 1198371, F₂, 7, 15) (dual of [(1198371, 7), 8388435, 16]-NRT-code), using
    - OOA 7-folding [i] based on linear OA(2¹⁶², 8388597, F₂, 15) (dual of [8388597, 8388435, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁴⁸, 2396870, F₂, 7, 14) (dual of [(2396870, 7), 16777842, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁴⁹, 2396870, F₂, 7, 15) (dual of [(2396870, 7), 16777841, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁸, 2396869, F₂, 8, 15) (dual of [(2396869, 8), 19174704, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(2²⁴⁸, 2396869, F₂, 21, 15) (dual of [(2396869, 21), 50334001, 16]-NRT-code)	[i]	OOA Stacking with Additional Row