MinT - Information on Result #1143439

Information on Result #1143439

Linear OOA(2²²², 2796358, F₂, 6, 12) (dual of [(2796358, 6), 16777926, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
  - 1 step truncation [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(2¹⁵⁸, 1398179, F₂, 6, 12) (dual of [(1398179, 6), 8388916, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁰, 79, F₂, 6, 6) (dual of [(79, 6), 454, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2²⁰, 79, F₂, 5, 6) (dual of [(79, 5), 375, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (14, 20, 79)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 1398100, F₂, 6, 12) (dual of [(1398100, 6), 8388462, 13]-NRT-code), using
    - OOA 6-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²², 2796357, F₂, 7, 12) (dual of [(2796357, 7), 19574277, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2²²², 2796357, F₂, 8, 12) (dual of [(2796357, 8), 22370634, 13]-NRT-code)	[i]
3	Linear OOA(2²²², 2796357, F₂, 18, 12) (dual of [(2796357, 18), 50334204, 13]-NRT-code)	[i]