MinT - Information on Result #661366

Information on Result #661366

Linear OA(16¹²², 560, F₁₆, 50) (dual of [560, 438, 51]-code), using trace code based on linear OA(256⁶¹, 280, F₂₅₆, 50) (dual of [280, 219, 51]-code), using

constructionÂ X applied to AG(F,103P) âŠ‚ AG(F,109P) [i] based on
1. linear OA(256⁵⁰, 257, F₂₅₆, 50) (dual of [257, 207, 51]-code or 257-arc in PG(49,256)), using algebraic-geometric code AG(F,103P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
2. linear OA(256³⁸, 257, F₂₅₆, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
3. linear OA(256¹¹, 23, F₂₅₆, 11) (dual of [23, 12, 12]-code or 23-arc in PG(10,256)), using
  - discarding factors / shortening the dual code based on linear OA(256¹¹, 256, F₂₅₆, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
    - Reedâ€“Solomon code RS(245,256) [i]

Mode: Constructive and 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 OA(16¹²³, 561, F₁₆, 50) (dual of [561, 438, 51]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(16¹²⁴, 562, F₁₆, 50) (dual of [562, 438, 51]-code)	[i]
3	Linear OA(16¹²⁵, 563, F₁₆, 50) (dual of [563, 438, 51]-code)	[i]
4	Linear OOA(16¹²², 280, F₁₆, 2, 50) (dual of [(280, 2), 438, 51]-NRT-code)	[i]	OOA Folding