MinT - Information on Result #1314252

Information on Result #1314252

Linear OA(16¹²⁶, 1041, F₁₆, 54) (dual of [1041, 915, 55]-code), using 12 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 11 times 0) based on linear OA(16¹²⁵, 1028, F₁₆, 54) (dual of [1028, 903, 55]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(16¹²⁴, 1026, F₁₆, 54) (dual of [1026, 902, 55]-code), using
  - trace code [i] based on linear OA(256⁶², 513, F₂₅₆, 54) (dual of [513, 451, 55]-code), using
    - extended algebraic-geometric code AG_e(F,458P) [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]
2. linear OA(16¹²⁴, 1027, F₁₆, 53) (dual of [1027, 903, 54]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16¹²⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 182134 111981 420724 348257 878194 904826 751861 179506 358632 144141 150739 989482 862846 490472 407677 553358 237271 715754 039460 097802 273160 412662 561705 707472 726016 [i]
3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 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]

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		This result only	Method
1	Linear OOA(16¹²⁶, 1032, F₁₆, 2, 54) (dual of [(1032, 2), 1938, 55]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (72, 126, 1032)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound