MinT - Information on Result #1789509

Information on Result #1789509

Digital (17, 22, 21512)-net over F₇, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7²², 21512, F₇, 5) (dual of [21512, 21490, 6]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(7⁰, 2801, F₇, 0) (dual of [2801, 2801, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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(7⁰, 2801, F₇, 0) (dual of [2801, 2801, 1]-code) (see above)
3. linear OA(7¹, 2801, F₇, 1) (dual of [2801, 2800, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
4. linear OA(7¹, 2801, F₇, 1) (dual of [2801, 2800, 2]-code) (see above)
5. linear OA(7¹, 2801, F₇, 1) (dual of [2801, 2800, 2]-code) (see above)
6. linear OA(7⁵, 2801, F₇, 2) (dual of [2801, 2796, 3]-code), using
  - Hamming code H(5,7) [i]
7. linear OA(7¹⁴, 4706, F₇, 5) (dual of [4706, 4692, 6]-code), using
  - trace code [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 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.