MinT - Information on Result #1016302

Information on Result #1016302

Linear OOA(9⁷⁵, 4391, F₉, 3, 17) (dual of [(4391, 3), 13098, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁹, 16, F₉, 3, 8) (dual of [(16, 3), 39, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,39P) [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(9⁶⁶, 4375, F₉, 3, 17) (dual of [(4375, 3), 13059, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁶⁶, 13125, F₉, 17) (dual of [13125, 13059, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁶⁶, 13126, F₉, 17) (dual of [13126, 13060, 18]-code), using
    - trace code [i] based on linear OA(81³³, 6563, F₈₁, 17) (dual of [6563, 6530, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
        linear OA(81³³, 6561, F₈₁, 17) (dual of [6561, 6528, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(81³¹, 6561, F₈₁, 16) (dual of [6561, 6530, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.