MinT - Information on Result #896753

Information on Result #896753

Linear OOA(8¹⁵⁰, 16434, F₈, 2, 29) (dual of [(16434, 2), 32718, 30]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²³, 45, F₈, 2, 14) (dual of [(45, 2), 67, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,75P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]
linear OOA(8¹²⁷, 16389, F₈, 2, 29) (dual of [(16389, 2), 32651, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8¹²⁷, 32778, F₈, 29) (dual of [32778, 32651, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹²⁷, 32779, F₈, 29) (dual of [32779, 32652, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
      1. 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]
      2. linear OA(8¹¹⁶, 32768, F₈, 27) (dual of [32768, 32652, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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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