MinT - Information on Result #1844715

Information on Result #1844715

OA(32⁷⁸, 263, S₃₂, 50), using discarding parts of the base based on linear OA(64⁶⁵, 263, F₆₄, 50) (dual of [263, 198, 51]-code), using

constructionÂ X applied to AG(F,205P) âŠ‚ AG(F,209P) [i] based on
1. linear OA(64⁶², 256, F₆₄, 50) (dual of [256, 194, 51]-code), using algebraic-geometric code AG(F,205P) [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
  - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]
2. linear OA(64⁵⁸, 256, F₆₄, 46) (dual of [256, 198, 47]-code), using algebraic-geometric code AG(F,209P) [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257 (see above)
3. linear OA(64³, 7, F₆₄, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
  - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
    - Reedâ€“Solomon code RS(61,64) [i]

Mode: Arbitrary.

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(32⁷⁹, 264, S₃₂, 50)	[i]		Code Embedding in Larger Space