MinT - Information on Result #898767

Information on Result #898767

Linear OOA(16¹⁰⁹, 2120, F₁₆, 2, 30) (dual of [(2120, 2), 4131, 31]-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, 2055, F₁₆, 2, 30) (dual of [(2055, 2), 4022, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁸, 4110, F₁₆, 30) (dual of [4110, 4022, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁸, 4111, F₁₆, 30) (dual of [4111, 4023, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(25) [i] based on
      1. 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]
      2. linear OA(16⁷³, 4096, F₁₆, 26) (dual of [4096, 4023, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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.