MinT - Information on Result #897654

Information on Result #897654

Linear OOA(9¹⁴⁰, 29562, F₉, 2, 27) (dual of [(29562, 2), 58984, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁸, 32, F₉, 2, 13) (dual of [(32, 2), 46, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,50P) [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(9¹²², 29530, F₉, 2, 27) (dual of [(29530, 2), 58938, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9¹²², 59060, F₉, 27) (dual of [59060, 58938, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹²², 59061, F₉, 27) (dual of [59061, 58939, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(9¹²¹, 59050, F₉, 27) (dual of [59050, 58929, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(9¹¹¹, 59050, F₉, 25) (dual of [59050, 58939, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(9¹, 11, F₉, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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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