MinT - Information on Result #1143532

Information on Result #1143532

Linear OOA(2²²¹, 2796328, F₂, 6, 13) (dual of [(2796328, 6), 16777747, 14]-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(2¹⁵⁷, 1398164, F₂, 6, 13) (dual of [(1398164, 6), 8388827, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁸, 64, F₂, 6, 6) (dual of [(64, 6), 366, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁸, 64, F₂, 5, 6) (dual of [(64, 5), 302, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 18, 64)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. 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(2²²¹, 2796327, F₂, 7, 13) (dual of [(2796327, 7), 19574068, 14]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2²²¹, 2796327, F₂, 8, 13) (dual of [(2796327, 8), 22370395, 14]-NRT-code)	[i]
3	Linear OOA(2²²¹, 2796327, F₂, 18, 13) (dual of [(2796327, 18), 50333665, 14]-NRT-code)	[i]