MinT - Information on Result #898614

Information on Result #898614

Linear OOA(16⁸⁸, 2114, F₁₆, 2, 25) (dual of [(2114, 2), 4140, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹⁸, 65, F₁₆, 2, 12) (dual of [(65, 2), 112, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,117P) [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(16⁷⁰, 2049, F₁₆, 2, 25) (dual of [(2049, 2), 4028, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁷⁰, 4098, F₁₆, 25) (dual of [4098, 4028, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁷⁰, 4099, F₁₆, 25) (dual of [4099, 4029, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(23) [i] based on
      1. 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]
      2. linear OA(16⁶⁷, 4096, F₁₆, 24) (dual of [4096, 4029, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [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.