MinT - Information on Result #1314242

Information on Result #1314242

Linear OA(16¹²⁵, 1085, F₁₆, 53) (dual of [1085, 960, 54]-code), using 55 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 11 times 0, 1, 42 times 0) based on linear OA(16¹²³, 1028, F₁₆, 53) (dual of [1028, 905, 54]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(16¹²², 1026, F₁₆, 53) (dual of [1026, 904, 54]-code), using
  - trace code [i] based on linear OA(256⁶¹, 513, F₂₅₆, 53) (dual of [513, 452, 54]-code), using
    - extended algebraic-geometric code AG_e(F,459P) [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(16¹²², 1027, F₁₆, 52) (dual of [1027, 905, 53]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16¹²²Â > V_b^sâˆ’1(kâˆ’1)Â = 647 541201 260657 039266 468286 788610 074332 352670 314324 999940 023904 646285 207970 657811 077217 014724 852149 279455 750443 066309 142089 083545 740416 644972 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(16¹²⁵, 1085, F₁₆, 2, 53) (dual of [(1085, 2), 2045, 54]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (72, 125, 1085)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound