MinT - Information on Result #1313092

Information on Result #1313092

Linear OA(9⁴⁷, 399, F₉, 18) (dual of [399, 352, 19]-code), using 121 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 8 times 0, 1, 26 times 0, 1, 38 times 0, 1, 45 times 0) based on linear OA(9⁴³, 274, F₉, 18) (dual of [274, 231, 19]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(9⁴², 272, F₉, 18) (dual of [272, 230, 19]-code), using
  - trace code [i] based on linear OA(81²¹, 136, F₈₁, 18) (dual of [136, 115, 19]-code), using
    - extended algebraic-geometric code AG_e(F,117P) [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]
2. linear OA(9⁴², 273, F₉, 17) (dual of [273, 231, 18]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9⁴²Â > V_b^sâˆ’1(kâˆ’1)Â = 7761 874144 032175 513657 339926 096418 973313 [i]
3. linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(9⁴⁷, 399, F₉, 2, 18) (dual of [(399, 2), 751, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(9⁴⁷, 399, F₉, 3, 18) (dual of [(399, 3), 1150, 19]-NRT-code)	[i]
3	Digital (29, 47, 399)-net over F₉	[i]