MinT - Information on Result #1733772

Information on Result #1733772

Digital (17, 22, 1179136)-net over F₁₆, using net defined by OOA based on linear OOA(16²², 1179136, F₁₆, 6, 5) (dual of [(1179136, 6), 7074794, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(16²², 1179137, F₁₆, 2, 5) (dual of [(1179137, 2), 2358252, 6]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] 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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.