MinT - Information on Result #896530

Information on Result #896530

Linear OOA(8⁸⁰, 1048603, F₈, 2, 12) (dual of [(1048603, 2), 2097126, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁹, 24, F₈, 2, 6) (dual of [(24, 2), 39, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,41P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁷¹, 1048579, F₈, 2, 12) (dual of [(1048579, 2), 2097087, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8⁷¹, 2097158, F₈, 12) (dual of [2097158, 2097087, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁷¹, 2097159, F₈, 12) (dual of [2097159, 2097088, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(8⁷¹, 2097152, F₈, 12) (dual of [2097152, 2097081, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(8⁶⁴, 2097152, F₈, 11) (dual of [2097152, 2097088, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 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.