MinT - Information on Result #1311632

Information on Result #1311632

Linear OA(7⁴⁸, 194, F₇, 20) (dual of [194, 146, 21]-code), using 7 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 6 times 0) based on linear OA(7⁴⁷, 186, F₇, 20) (dual of [186, 139, 21]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(7⁴⁶, 184, F₇, 20) (dual of [184, 138, 21]-code), using
  - trace code [i] based on linear OA(49²³, 92, F₄₉, 20) (dual of [92, 69, 21]-code), using
    - extended algebraic-geometric code AG_e(F,71P) [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
      - a curve from the manYPoints database [i]
2. linear OA(7⁴⁶, 185, F₇, 19) (dual of [185, 139, 20]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁴⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 399 774349 870480 568364 754807 415121 804097 [i]
3. linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 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]

Mode: 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

The following results depend on this result:

	Result		Method
1	Linear OOA(7⁴⁸, 193, F₇, 2, 20) (dual of [(193, 2), 338, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(7⁴⁸, 193, F₇, 3, 20) (dual of [(193, 3), 531, 21]-NRT-code)	[i]
3	Digital (28, 48, 193)-net over F₇	[i]