MinT - Information on Result #896591

Information on Result #896591

Linear OOA(8⁸⁸, 16410, F₈, 2, 18) (dual of [(16410, 2), 32732, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹², 24, F₈, 2, 9) (dual of [(24, 2), 36, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,38P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁷⁶, 16386, F₈, 2, 18) (dual of [(16386, 2), 32696, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8⁷⁶, 32772, F₈, 18) (dual of [32772, 32696, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁷⁶, 32773, F₈, 18) (dual of [32773, 32697, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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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