MinT - Information on Result #898872

Information on Result #898872

Linear OOA(16¹¹⁷, 2114, F₁₆, 2, 34) (dual of [(2114, 2), 4111, 35]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²³, 65, F₁₆, 2, 17) (dual of [(65, 2), 107, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,112P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OOA(16⁹⁴, 2049, F₁₆, 2, 34) (dual of [(2049, 2), 4004, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹⁴, 4098, F₁₆, 34) (dual of [4098, 4004, 35]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹⁴, 4099, F₁₆, 34) (dual of [4099, 4005, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(32) [i] based on
      1. linear OA(16⁹⁴, 4096, F₁₆, 34) (dual of [4096, 4002, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. linear OA(16⁹¹, 4096, F₁₆, 33) (dual of [4096, 4005, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      3. linear OA(16⁰, 3, F₁₆, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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.