MinT - Information on Result #906442

Information on Result #906442

Linear OOA(5⁹³, 4194396, F₅, 2, 11) (dual of [(4194396, 2), 8388699, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹², 95, F₅, 2, 5) (dual of [(95, 2), 178, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹, 31, F₅, 2, 1) (dual of [(31, 2), 61, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
      - Hamming code H(3,5) [i]
  3. linear OOA(5⁸, 33, F₅, 2, 5) (dual of [(33, 2), 58, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 8, 33)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5⁸¹, 4194301, F₅, 2, 11) (dual of [(4194301, 2), 8388521, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5⁸¹, 8388602, F₅, 11) (dual of [8388602, 8388521, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

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