MinT - Information on Result #1845677

Information on Result #1845677

OA(64⁴⁸, 323, S₆₄, 33), using discarding parts of the base based on linear OA(256³⁶, 323, F₂₅₆, 33) (dual of [323, 287, 34]-code), using

constructionÂ X applied to AG(F,286P) âŠ‚ AG(F,288P) [i] based on
1. linear OA(256³⁵, 320, F₂₅₆, 33) (dual of [320, 285, 34]-code), using algebraic-geometric code AG(F,286P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
  - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(256³³, 320, F₂₅₆, 31) (dual of [320, 287, 32]-code), using algebraic-geometric code AG(F,288P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 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(64⁴⁹, 324, S₆₄, 33)	[i]		Code Embedding in Larger Space
2	OA(64⁵⁰, 325, S₆₄, 33)	[i]		Code Embedding in Larger Space