MinT - Information on Result #1159847

Information on Result #1159847

Linear OOA(2²¹³, 1198431, F₂, 7, 16) (dual of [(1198431, 7), 8388804, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 60, F₂, 7, 8) (dual of [(60, 7), 391, 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(2¹⁹, 30, F₂, 7, 8) (dual of [(30, 7), 191, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (11, 19, 30)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁴, 1198371, F₂, 7, 16) (dual of [(1198371, 7), 8388413, 17]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2¹⁸⁴, 8388597, F₂, 16) (dual of [8388597, 8388413, 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.

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