MinT - Information on Result #1015083

Information on Result #1015083

Linear OOA(8¹⁶⁸, 87407, F₈, 3, 29) (dual of [(87407, 3), 262053, 30]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁷, 24, F₈, 3, 14) (dual of [(24, 3), 55, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,57P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹⁵¹, 87383, F₈, 3, 29) (dual of [(87383, 3), 261998, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁵¹, 262149, F₈, 29) (dual of [262149, 261998, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁵¹, 262150, F₈, 29) (dual of [262150, 261999, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(8¹⁵¹, 262144, F₈, 29) (dual of [262144, 261993, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(8¹⁴⁵, 262144, F₈, 28) (dual of [262144, 261999, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(8⁰, 6, F₈, 0) (dual of [6, 6, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.