MinT - Information on Result #897610

Information on Result #897610

Linear OOA(9¹⁰⁵, 29558, F₉, 2, 21) (dual of [(29558, 2), 59011, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹³, 28, F₉, 2, 10) (dual of [(28, 2), 43, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,45P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9⁹², 29530, F₉, 2, 21) (dual of [(29530, 2), 58968, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁹², 59060, F₉, 21) (dual of [59060, 58968, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁹², 59061, F₉, 21) (dual of [59061, 58969, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(9⁹¹, 59050, F₉, 21) (dual of [59050, 58959, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(9⁸¹, 59050, F₉, 19) (dual of [59050, 58969, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 9¹⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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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