MinT - Information on Result #1014992

Information on Result #1014992

Linear OOA(8¹⁴⁹, 87407, F₈, 3, 26) (dual of [(87407, 3), 262072, 27]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁶, 24, F₈, 3, 13) (dual of [(24, 3), 56, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,58P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹³³, 87383, F₈, 3, 26) (dual of [(87383, 3), 262016, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹³³, 262149, F₈, 26) (dual of [262149, 262016, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹³³, 262150, F₈, 26) (dual of [262150, 262017, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
      1. linear OA(8¹³³, 262144, F₈, 26) (dual of [262144, 262011, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(8¹²⁷, 262144, F₈, 25) (dual of [262144, 262017, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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.