MinT - Information on Result #1015105

Information on Result #1015105

Linear OOA(8¹⁴⁹, 10948, F₈, 3, 30) (dual of [(10948, 3), 32695, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁸, 24, F₈, 3, 15) (dual of [(24, 3), 54, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,56P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹³¹, 10924, F₈, 3, 30) (dual of [(10924, 3), 32641, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹³¹, 32772, F₈, 30) (dual of [32772, 32641, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹³¹, 32773, F₈, 30) (dual of [32773, 32642, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(8¹³¹, 32768, F₈, 30) (dual of [32768, 32637, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(8¹²⁶, 32768, F₈, 29) (dual of [32768, 32642, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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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