MinT - Information on Result #896549

Information on Result #896549

Linear OOA(8⁷², 16413, F₈, 2, 14) (dual of [(16413, 2), 32754, 15]-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(8⁶², 16389, F₈, 2, 14) (dual of [(16389, 2), 32716, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8⁶², 32778, F₈, 14) (dual of [32778, 32716, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁶², 32779, F₈, 14) (dual of [32779, 32717, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(11) [i] based on
      1. 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]
      2. linear OA(8⁵¹, 32768, F₈, 12) (dual of [32768, 32717, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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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