MinT - Information on Result #856061

Information on Result #856061

Linear OOA(16²², 589568, F₁₆, 2, 5) (dual of [(589568, 2), 1179114, 6]-NRT-code), using OOA 2-folding based on linear OA(16²², 1179136, F₁₆, 5) (dual of [1179136, 1179114, 6]-code), using

discarding factors / shortening the dual code based on linear OA(16²², 1179137, F₁₆, 5) (dual of [1179137, 1179115, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 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]
  2. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  3. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  4. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  5. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  6. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  7. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  8. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  9. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  10. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  11. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
  12. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 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]
  13. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
  14. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
  15. linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
    - Hamming code H(5,16) [i]
  16. linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
    - trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [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.