MinT - Information on Result #660498

Information on Result #660498

Linear OA(8¹⁶⁸, 1038, F₈, 53) (dual of [1038, 870, 54]-code), using trace code based on linear OA(64⁸⁴, 519, F₆₄, 53) (dual of [519, 435, 54]-code), using

constructionÂ X applied to AG(F,458P) âŠ‚ AG(F,462P) [i] based on
1. linear OA(64⁸¹, 512, F₆₄, 53) (dual of [512, 431, 54]-code), using algebraic-geometric code AG(F,458P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
  - the Hermitian function field over F₆₄ [i]
2. linear OA(64⁷⁷, 512, F₆₄, 49) (dual of [512, 435, 50]-code), using algebraic-geometric code AG(F,462P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (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: Constructive and linear.

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	Linear OA(8¹⁶⁹, 1039, F₈, 53) (dual of [1039, 870, 54]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(8¹⁶⁸, 519, F₈, 2, 53) (dual of [(519, 2), 870, 54]-NRT-code)	[i]		OOA Folding