MinT - Information on Result #640811

Information on Result #640811

Linear OA(2²⁰¹, 214, F₂, 92) (dual of [214, 13, 93]-code), using juxtaposition based on

linear OA(2¹⁰, 23, F₂, 4) (dual of [23, 13, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁰, 32, F₂, 4) (dual of [32, 22, 5]-code), using
  - 1 times truncation [i] based on linear OA(2¹¹, 33, F₂, 5) (dual of [33, 22, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33Â | 2¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OA(2¹⁷⁸, 191, F₂, 87) (dual of [191, 13, 88]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁷⁸, 192, F₂, 87) (dual of [192, 14, 88]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4⁵⁷, 64, F₄, 43) (dual of [64, 7, 44]-code), using
      - an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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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