MinT - Information on Result #1014614

Information on Result #1014614

Linear OOA(8¹¹¹, 699079, F₈, 3, 16) (dual of [(699079, 3), 2097126, 17]-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(8¹⁰⁰, 699055, F₈, 3, 16) (dual of [(699055, 3), 2097065, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁰⁰, 2097165, F₈, 16) (dual of [2097165, 2097065, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁰⁰, 2097167, F₈, 16) (dual of [2097167, 2097067, 17]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(13) [i] based on
      1. linear OA(8⁹⁹, 2097152, F₈, 17) (dual of [2097152, 2097053, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(8⁸⁵, 2097152, F₈, 14) (dual of [2097152, 2097067, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(8¹, 15, F₈, 1) (dual of [15, 14, 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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