MinT - Information on Result #1010588

Information on Result #1010588

Linear OOA(3¹³⁴, 3188657, F₃, 3, 11) (dual of [(3188657, 3), 9565837, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 3, 5) (dual of [(7, 3), 15, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,15P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹²⁸, 3188650, F₃, 3, 11) (dual of [(3188650, 3), 9565822, 12]-NRT-code), using
- trace code [i] based on linear OOA(9⁶⁴, 1594325, F₉, 3, 11) (dual of [(1594325, 3), 4782911, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(9⁶⁴, 4782975, F₉, 11) (dual of [4782975, 4782911, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁶⁴, 4782976, F₉, 11) (dual of [4782976, 4782912, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        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, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.