MinT - Information on Result #2273624

Information on Result #2273624

Linear OA(4¹⁶⁰, 544, F₄, 44) (dual of [544, 384, 45]-code), using 1 times code embedding in larger space based on linear OA(4¹⁵⁹, 543, F₄, 44) (dual of [543, 384, 45]-code), using

trace code [i] based on linear OA(64⁵³, 181, F₆₄, 44) (dual of [181, 128, 45]-code), using
- constructionÂ X applied to AG(F,131P) âŠ‚ AG(F,134P) [i] based on
  1. linear OA(64⁵¹, 176, F₆₄, 44) (dual of [176, 125, 45]-code), using algebraic-geometric code AG(F,131P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(64⁴⁸, 176, F₆₄, 41) (dual of [176, 128, 42]-code), using algebraic-geometric code AG(F,134P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OA(64², 5, F₆₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,64)), using
    - discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
      - Reedâ€“Solomon code RS(62,64) [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 OOA(4¹⁶⁰, 272, F₄, 2, 44) (dual of [(272, 2), 384, 45]-NRT-code)	[i]		OOA Folding