MinT - Information on Result #1175899

Information on Result #1175899

Linear OOA(2²³⁹, 1048633, F₂, 8, 19) (dual of [(1048633, 8), 8388825, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³¹, 58, F₂, 8, 9) (dual of [(58, 8), 433, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 32, F₂, 8, 4) (dual of [(32, 8), 246, 5]-NRT-code), using
    - appending 4 arbitrary columns [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²¹, 29, F₂, 8, 9) (dual of [(29, 8), 211, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 21, 29)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2²⁰⁸, 1048575, F₂, 8, 19) (dual of [(1048575, 8), 8388392, 20]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2²⁰⁸, 8388600, F₂, 19) (dual of [8388600, 8388392, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁹, 1048633, F₂, 8, 18) (dual of [(1048633, 8), 8388825, 19]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁴⁰, 1048633, F₂, 8, 19) (dual of [(1048633, 8), 8388824, 20]-NRT-code)	[i]		OOA Duplication