MinT - Information on Result #1159749

Information on Result #1159749

Linear OOA(2²⁵², 2397250, F₂, 7, 14) (dual of [(2397250, 7), 16780498, 15]-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(2¹⁸⁷, 1198625, F₂, 7, 14) (dual of [(1198625, 7), 8390188, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁶, 254, F₂, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
  2. linear OOA(2¹⁶¹, 1198371, F₂, 7, 14) (dual of [(1198371, 7), 8388436, 15]-NRT-code), using
    - OOA 7-folding [i] based on linear OA(2¹⁶¹, 8388597, F₂, 14) (dual of [8388597, 8388436, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁴, 2397250, F₂, 7, 14) (dual of [(2397250, 7), 16780496, 15]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵², 2397249, F₂, 8, 14) (dual of [(2397249, 8), 19177740, 15]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(2²⁵², 2397249, F₂, 21, 14) (dual of [(2397249, 21), 50341977, 15]-NRT-code)	[i]	OOA Stacking with Additional Row