MinT - Information on Result #660507

Information on Result #660507

Linear OA(8¹⁷⁰, 1046, F₈, 52) (dual of [1046, 876, 53]-code), using trace code based on linear OA(64⁸⁵, 523, F₆₄, 52) (dual of [523, 438, 53]-code), using

constructionÂ X applied to AG(F,459P) âŠ‚ AG(F,465P) [i] based on
1. linear OA(64⁸⁰, 512, F₆₄, 52) (dual of [512, 432, 53]-code), using algebraic-geometric code AG(F,459P) [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(64⁷⁴, 512, F₆₄, 46) (dual of [512, 438, 47]-code), using algebraic-geometric code AG(F,465P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OA(64⁵, 11, F₆₄, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,64)), using
  - discarding factors / shortening the dual code based on linear OA(64⁵, 64, F₆₄, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
    - Reedâ€“Solomon code RS(59,64) [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(8¹⁷¹, 1047, F₈, 52) (dual of [1047, 876, 53]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(8¹⁷⁰, 523, F₈, 2, 52) (dual of [(523, 2), 876, 53]-NRT-code)	[i]		OOA Folding