MinT - Information on Result #731962

Information on Result #731962

Linear OA(16¹²⁶, 4170, F₁₆, 36) (dual of [4170, 4044, 37]-code), using (u,Â u+v)-construction based on

linear OA(16²⁵, 67, F₁₆, 18) (dual of [67, 42, 19]-code), using
- constructionÂ X applied to AG(F,45P) âŠ‚ AG(F,47P) [i] based on
  1. linear OA(16²⁴, 64, F₁₆, 18) (dual of [64, 40, 19]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OA(16²², 64, F₁₆, 16) (dual of [64, 42, 17]-code), using algebraic-geometric code AG(F,47P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(16¹⁰¹, 4103, F₁₆, 36) (dual of [4103, 4002, 37]-code), using
- constructionÂ X applied to C_e(35) âŠ‚ C_e(33) [i] based on
  1. linear OA(16¹⁰⁰, 4096, F₁₆, 36) (dual of [4096, 3996, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
  2. linear OA(16⁹⁴, 4096, F₁₆, 34) (dual of [4096, 4002, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
  3. linear OA(16¹, 7, F₁₆, 1) (dual of [7, 6, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)

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.