MinT - Information on Result #1014661

Information on Result #1014661

Linear OOA(8⁹⁷, 87407, F₈, 3, 17) (dual of [(87407, 3), 262124, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹¹, 24, F₈, 3, 8) (dual of [(24, 3), 61, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,63P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁸⁶, 87383, F₈, 3, 17) (dual of [(87383, 3), 262063, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁸⁶, 262149, F₈, 17) (dual of [262149, 262063, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁸⁶, 262151, F₈, 17) (dual of [262151, 262065, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
      1. linear OA(8⁸⁵, 262144, F₈, 17) (dual of [262144, 262059, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(8⁷⁹, 262144, F₈, 15) (dual of [262144, 262065, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(8¹, 7, F₈, 1) (dual of [7, 6, 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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