MinT - Information on Result #1815863

Information on Result #1815863

OA(16⁸⁵, 128, S₁₆, 53), using discarding parts of the base based on linear OA(32⁶⁸, 128, F₃₂, 53) (dual of [128, 60, 54]-code), using

constructionÂ X applied to AG(F,65P) âŠ‚ AG(F,70P) [i] based on
1. linear OA(32⁶⁴, 119, F₃₂, 53) (dual of [119, 55, 54]-code), using algebraic-geometric code AG(F,65P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]
2. linear OA(32⁵⁹, 119, F₃₂, 48) (dual of [119, 60, 49]-code), using algebraic-geometric code AG(F,70P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (see above)
3. linear OA(32⁴, 9, F₃₂, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,32)), using
  - discarding factors / shortening the dual code based on linear OA(32⁴, 32, F₃₂, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
    - Reedâ€“Solomon code RS(28,32) [i]

Mode: Constructive.

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	OA(16⁸⁶, 129, S₁₆, 53)	[i]		Code Embedding in Larger Space
2	OA(16⁸⁷, 130, S₁₆, 53)	[i]		Code Embedding in Larger Space