MinT - Information on Result #1314261

Information on Result #1314261

Linear OA(16¹²⁹, 1080, F₁₆, 55) (dual of [1080, 951, 56]-code), using 50 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 10 times 0, 1, 38 times 0) based on linear OA(16¹²⁷, 1028, F₁₆, 55) (dual of [1028, 901, 56]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(16¹²⁶, 1026, F₁₆, 55) (dual of [1026, 900, 56]-code), using
  - trace code [i] based on linear OA(256⁶³, 513, F₂₅₆, 55) (dual of [513, 450, 56]-code), using
    - extended algebraic-geometric code AG_e(F,457P) [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(16¹²⁶, 1027, F₁₆, 54) (dual of [1027, 901, 55]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16¹²⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 50 210790 698738 752486 317399 364186 941159 934807 596008 383676 989017 812331 765289 235222 248624 068592 070976 287060 287791 823211 609399 347728 684299 524596 332472 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		Method
1	Linear OOA(16¹²⁹, 1080, F₁₆, 2, 55) (dual of [(1080, 2), 2031, 56]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (74, 129, 1080)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(16¹²⁹, 540, F₁₆, 2, 55) (dual of [(540, 2), 951, 56]-NRT-code)	[i]	OOA Folding