MinT - Information on Result #1079638

Information on Result #1079638

Linear OOA(2¹⁸⁰, 2105342, F₂, 4, 12) (dual of [(2105342, 4), 8421188, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁰, 8191, F₂, 4, 6) (dual of [(8191, 4), 32724, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F₂, using
  - 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁴⁰, 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 4194302, F₂, 2, 12) (dual of [(4194302, 2), 8388464, 13]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 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		This result only	Method
1	Linear OOA(2²⁴⁷, 4210684, F₂, 4, 12) (dual of [(4210684, 4), 16842489, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁴⁴, 4202492, F₂, 4, 12) (dual of [(4202492, 4), 16809724, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs