MinT - Information on Result #898736

Information on Result #898736

Linear OOA(16¹⁰⁴, 2118, F₁₆, 2, 29) (dual of [(2118, 2), 4132, 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(16⁸⁴, 2053, F₁₆, 2, 29) (dual of [(2053, 2), 4022, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁴, 4106, F₁₆, 29) (dual of [4106, 4022, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁴, 4107, F₁₆, 29) (dual of [4107, 4023, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(25) [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(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(16², 11, F₁₆, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,16)), using
        discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [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.