MinT - Information on Result #898794

Information on Result #898794

Linear OOA(16¹⁰⁹, 2114, F₁₆, 2, 31) (dual of [(2114, 2), 4119, 32]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²¹, 65, F₁₆, 2, 15) (dual of [(65, 2), 109, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,114P) [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(16⁸⁸, 2049, F₁₆, 2, 31) (dual of [(2049, 2), 4010, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁸, 4098, F₁₆, 31) (dual of [4098, 4010, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁸, 4099, F₁₆, 31) (dual of [4099, 4011, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(29) [i] based on
      1. linear OA(16⁸⁸, 4096, F₁₆, 31) (dual of [4096, 4008, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(16⁸⁵, 4096, F₁₆, 30) (dual of [4096, 4011, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [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.