MinT - Information on Result #1117872

Information on Result #1117872

Linear OOA(3¹⁵³, 11821, F₃, 5, 21) (dual of [(11821, 5), 58952, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹¹, 7, F₃, 5, 10) (dual of [(7, 5), 24, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,24P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁴², 11814, F₃, 5, 21) (dual of [(11814, 5), 58928, 22]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁴², 59070, F₃, 21) (dual of [59070, 58928, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁴², 59071, F₃, 21) (dual of [59071, 58929, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹⁴¹, 59050, F₃, 21) (dual of [59050, 58909, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(3¹²¹, 59050, F₃, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(3¹, 21, F₃, 1) (dual of [21, 20, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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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