MinT - Information on Result #1845269

Information on Result #1845269

OA(27⁹⁶, 246, S₂₇, 62), using discarding parts of the base based on linear OA(81⁷², 246, F₈₁, 62) (dual of [246, 174, 63]-code), using

constructionÂ X applied to AG(F,180P) âŠ‚ AG(F,182P) [i] based on
1. linear OA(81⁷¹, 243, F₈₁, 62) (dual of [243, 172, 63]-code), using algebraic-geometric code AG(F,180P) [i] based on function field F/F₈₁ with g(F) = 9 and N(F) ≥ 244, using
  - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₈₁ [i]
2. linear OA(81⁶⁹, 243, F₈₁, 60) (dual of [243, 174, 61]-code), using algebraic-geometric code AG(F,182P) [i] based on function field F/F₈₁ with g(F) = 9 and N(F) ≥ 244 (see above)
3. linear OA(81¹, 3, F₈₁, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 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(27⁹⁷, 247, S₂₇, 62)	[i]		Code Embedding in Larger Space
2	OA(27⁹⁸, 248, S₂₇, 62)	[i]		Code Embedding in Larger Space