MinT - Information on Result #2765599

Information on Result #2765599

Linear OOA(2²¹⁹, 2097229, F₂, 4, 16) (dual of [(2097229, 4), 8388697, 17]-NRT-code), using strength reduction based on linear OOA(2²¹⁹, 2097229, F₂, 4, 17) (dual of [(2097229, 4), 8388697, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³², 78, F₂, 4, 8) (dual of [(78, 4), 280, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹¹, 47, F₂, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹¹, 47, F₂, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2²¹, 39, F₂, 4, 8) (dual of [(39, 4), 135, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
        linear code embedding found in a computer search [i]
2. linear OOA(2¹⁸⁷, 2097151, F₂, 4, 17) (dual of [(2097151, 4), 8388417, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁸⁷, 4194302, F₂, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.