MinT - Information on Result #1014836

Information on Result #1014836

Linear OOA(8¹⁰⁵, 10950, F₈, 3, 21) (dual of [(10950, 3), 32745, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹³, 24, F₈, 3, 10) (dual of [(24, 3), 59, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,61P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁹², 10926, F₈, 3, 21) (dual of [(10926, 3), 32686, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁹², 32778, F₈, 21) (dual of [32778, 32686, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁹², 32780, F₈, 21) (dual of [32780, 32688, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(8⁹¹, 32769, F₈, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(8⁸¹, 32769, F₈, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 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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