MinT - Information on Result #1844762

Information on Result #1844762

OA(32⁸⁴, 259, S₃₂, 57), using discarding parts of the base based on linear OA(64⁷⁰, 259, F₆₄, 57) (dual of [259, 189, 58]-code), using

constructionÂ X applied to AG(F,198P) âŠ‚ AG(F,200P) [i] based on
1. linear OA(64⁶⁹, 256, F₆₄, 57) (dual of [256, 187, 58]-code), using algebraic-geometric code AG(F,198P) [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(64⁶⁷, 256, F₆₄, 55) (dual of [256, 189, 56]-code), using algebraic-geometric code AG(F,200P) [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257 (see above)
3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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(32⁸⁵, 260, S₃₂, 57)	[i]		Code Embedding in Larger Space
2	OA(32⁸⁶, 261, S₃₂, 57)	[i]		Code Embedding in Larger Space