MinT - Information on Result #1015921

Information on Result #1015921

Linear OOA(9³⁵, 4391, F₉, 3, 8) (dual of [(4391, 3), 13138, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁵, 16, F₉, 3, 4) (dual of [(16, 3), 43, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,43P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(9³⁰, 4375, F₉, 3, 8) (dual of [(4375, 3), 13095, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9³⁰, 13125, F₉, 8) (dual of [13125, 13095, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(9³⁰, 13126, F₉, 8) (dual of [13126, 13096, 9]-code), using
    - trace code [i] based on linear OA(81¹⁵, 6563, F₈₁, 8) (dual of [6563, 6548, 9]-code), using
      - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(81¹⁵, 6561, F₈₁, 8) (dual of [6561, 6546, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(81¹³, 6561, F₈₁, 7) (dual of [6561, 6548, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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.