MinT - Information on Result #1621060

Information on Result #1621060

Linear OOA(3¹⁹², 1775173, F₃, 5, 18) (dual of [(1775173, 5), 8875673, 19]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁹², 3550346, F₃, 3, 18) (dual of [(3550346, 3), 10650846, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹², 3550347, F₃, 3, 18) (dual of [(3550347, 3), 10650849, 19]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁹², 3550347, F₃, 2, 18) (dual of [(3550347, 2), 7100502, 19]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁹², 4194311, F₃, 2, 18) (dual of [(4194311, 2), 8388430, 19]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3¹², 10, F₃, 2, 9) (dual of [(10, 2), 8, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
        OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.