MinT - Information on Result #1009206

Information on Result #1009206

Linear OOA(2²³⁰, 5592662, F₂, 3, 13) (dual of [(5592662, 3), 16777756, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁷, 4194302, F₂, 3, 6) (dual of [(4194302, 3), 12582839, 7]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁶³, 2796331, F₂, 3, 13) (dual of [(2796331, 3), 8388830, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁴, 130, F₂, 3, 6) (dual of [(130, 3), 366, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³, 3, F₂, 3, 3) (dual of [(3, 3), 6, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;6,2) [i]
      2. linear OOA(2²¹, 127, F₂, 3, 6) (dual of [(127, 3), 360, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁹, 2796201, F₂, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
    - OOA 3-folding [i] 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		This result only	Method
1	Linear OOA(2²³⁰, 2796331, F₂, 5, 13) (dual of [(2796331, 5), 13981425, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³⁰, 2796331, F₂, 6, 13) (dual of [(2796331, 6), 16777756, 14]-NRT-code)	[i]		OOA Folding