MinT - Information on Result #908526

Information on Result #908526

Linear OOA(2²⁰⁹, 112, F₂, 2, 96) (dual of [(112, 2), 15, 97]-NRT-code), using juxtaposition based on

linear OOA(2¹⁵, 15, F₂, 2, 8) (dual of [(15, 2), 15, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁵, 16, F₂, 2, 8) (dual of [(16, 2), 17, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 15, 16)-net over F₂, using
    - linear code embedding found in a computer search [i]
linear OOA(2¹⁷⁹, 97, F₂, 2, 87) (dual of [(97, 2), 15, 88]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁷⁹, 194, F₂, 87) (dual of [194, 15, 88]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁷⁹, 195, F₂, 87) (dual of [195, 16, 88]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(4⁵⁷, 65, F₄, 43) (dual of [65, 8, 44]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

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