MinT - Information on Result #898737

Information on Result #898737

Linear OOA(16¹⁰⁵, 2120, F₁₆, 2, 29) (dual of [(2120, 2), 4135, 30]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²⁰, 65, F₁₆, 2, 14) (dual of [(65, 2), 110, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,115P) [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(16⁸⁵, 2055, F₁₆, 2, 29) (dual of [(2055, 2), 4025, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁵, 4110, F₁₆, 29) (dual of [4110, 4025, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁵, 4111, F₁₆, 29) (dual of [4111, 4026, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(24) [i] based on
      1. linear OA(16⁸², 4096, F₁₆, 29) (dual of [4096, 4014, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(16⁷⁰, 4096, F₁₆, 25) (dual of [4096, 4026, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(16³, 15, F₁₆, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-cap in PG(2,16)), using
        discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [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.