MinT - Information on Result #2274836

Information on Result #2274836

Linear OA(4²⁵³, 562, F₄, 72) (dual of [562, 309, 73]-code), using 1 times code embedding in larger space based on linear OA(4²⁵², 561, F₄, 72) (dual of [561, 309, 73]-code), using

trace code [i] based on linear OA(64⁸⁴, 187, F₆₄, 72) (dual of [187, 103, 73]-code), using
- constructionÂ X applied to AG(F,103P) âŠ‚ AG(F,109P) [i] based on
  1. linear OA(64⁷⁹, 176, F₆₄, 72) (dual of [176, 97, 73]-code), using algebraic-geometric code AG(F,103P) [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(64⁷³, 176, F₆₄, 66) (dual of [176, 103, 67]-code), using algebraic-geometric code AG(F,109P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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 OOA(4²⁵³, 281, F₄, 2, 72) (dual of [(281, 2), 309, 73]-NRT-code)	[i]		OOA Folding