MinT - Information on Result #661324

Information on Result #661324

Linear OA(16¹¹⁴, 552, F₁₆, 48) (dual of [552, 438, 49]-code), using trace code based on linear OA(256⁵⁷, 276, F₂₅₆, 48) (dual of [276, 219, 49]-code), using

constructionÂ X applied to AG(F,104P) âŠ‚ AG(F,109P) [i] based on
1. linear OA(256⁴⁸, 257, F₂₅₆, 48) (dual of [257, 209, 49]-code or 257-arc in PG(47,256)), using algebraic-geometric code AG(F,104P) 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(256⁹, 19, F₂₅₆, 9) (dual of [19, 10, 10]-code or 19-arc in PG(8,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁹, 256, F₂₅₆, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
    - Reedâ€“Solomon code RS(247,256) [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(16¹¹⁵, 553, F₁₆, 48) (dual of [553, 438, 49]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(16¹¹⁶, 554, F₁₆, 48) (dual of [554, 438, 49]-code)	[i]
3	Linear OA(16¹¹⁷, 555, F₁₆, 48) (dual of [555, 438, 49]-code)	[i]
4	Linear OOA(16¹¹⁴, 276, F₁₆, 2, 48) (dual of [(276, 2), 438, 49]-NRT-code)	[i]	OOA Folding