MinT - Information on Result #660446

Information on Result #660446

Linear OA(8¹⁶⁰, 1042, F₈, 48) (dual of [1042, 882, 49]-code), using trace code based on linear OA(64⁸⁰, 521, F₆₄, 48) (dual of [521, 441, 49]-code), using

constructionÂ X applied to AG(F,463P) âŠ‚ AG(F,468P) [i] based on
1. linear OA(64⁷⁶, 512, F₆₄, 48) (dual of [512, 436, 49]-code), using algebraic-geometric code AG(F,463P) [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(64⁷¹, 512, F₆₄, 43) (dual of [512, 441, 44]-code), using algebraic-geometric code AG(F,468P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OA(64⁴, 9, F₆₄, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,64)), using
  - discarding factors / shortening the dual code based on linear OA(64⁴, 64, F₆₄, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
    - Reedâ€“Solomon code RS(60,64) [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(8¹⁶¹, 1043, F₈, 48) (dual of [1043, 882, 49]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(8¹⁶⁰, 521, F₈, 2, 48) (dual of [(521, 2), 882, 49]-NRT-code)	[i]		OOA Folding