MinT - Information on Result #896555

Information on Result #896555

Linear OOA(8⁷⁶, 16410, F₈, 2, 15) (dual of [(16410, 2), 32744, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁰, 24, F₈, 2, 7) (dual of [(24, 2), 38, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,40P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁶⁶, 16386, F₈, 2, 15) (dual of [(16386, 2), 32706, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8⁶⁶, 32772, F₈, 15) (dual of [32772, 32706, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁶⁶, 32773, F₈, 15) (dual of [32773, 32707, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
      1. linear OA(8⁶⁶, 32768, F₈, 15) (dual of [32768, 32702, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(8⁶¹, 32768, F₈, 14) (dual of [32768, 32707, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

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