MinT - Information on Result #1175746

Information on Result #1175746

Linear OOA(2²¹⁴, 1048642, F₂, 8, 16) (dual of [(1048642, 8), 8388922, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁰, 67, F₂, 8, 8) (dual of [(67, 8), 506, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2³⁰, 67, F₂, 7, 8) (dual of [(67, 7), 439, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁰, 32, F₂, 7, 4) (dual of [(32, 7), 214, 5]-NRT-code), using
      - appending 3 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(2²⁰, 35, F₂, 7, 8) (dual of [(35, 7), 225, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 20, 35)-net over F₂, using
        linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁴, 1048575, F₂, 8, 16) (dual of [(1048575, 8), 8388416, 17]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹⁴, 1048641, F₂, 24, 16) (dual of [(1048641, 24), 25167170, 17]-NRT-code)	[i]		OOA Stacking with Additional Row