MinT - Information on Result #661188

Information on Result #661188

Linear OA(16⁸⁴, 536, F₁₆, 37) (dual of [536, 452, 38]-code), using trace code based on linear OA(256⁴², 268, F₂₅₆, 37) (dual of [268, 226, 38]-code), using

constructionÂ X applied to AG(F, Q+108P) âŠ‚ AG(F, Q+111P) [i] based on
1. linear OA(256³⁷, 257, F₂₅₆, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using algebraic-geometric code AG(F, Q+108P) with degQ = 3 and 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(256³¹, 257, F₂₅₆, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using algebraic-geometric code AG(F, Q+111P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
3. linear OA(256⁵, 11, F₂₅₆, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,256)), using
  - discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
    - Reedâ€“Solomon code RS(251,256) [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(16⁸⁵, 537, F₁₆, 37) (dual of [537, 452, 38]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(16⁸⁶, 538, F₁₆, 37) (dual of [538, 452, 38]-code)	[i]
3	Linear OA(16⁸⁷, 539, F₁₆, 37) (dual of [539, 452, 38]-code)	[i]
4	Linear OOA(16⁸⁴, 268, F₁₆, 2, 37) (dual of [(268, 2), 452, 38]-NRT-code)	[i]	OOA Folding