MinT - Information on Result #1016420

Information on Result #1016420

Linear OOA(9¹⁴⁰, 1594353, F₉, 3, 21) (dual of [(1594353, 3), 4782919, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹³, 28, F₉, 3, 10) (dual of [(28, 3), 71, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,73P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9¹²⁷, 1594325, F₉, 3, 21) (dual of [(1594325, 3), 4782848, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9¹²⁷, 4782975, F₉, 21) (dual of [4782975, 4782848, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹²⁷, 4782976, F₉, 21) (dual of [4782976, 4782849, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
      1. linear OA(9¹²⁷, 4782969, F₉, 21) (dual of [4782969, 4782842, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(9¹²⁰, 4782969, F₉, 20) (dual of [4782969, 4782849, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.