MinT - Information on Result #2274160

Information on Result #2274160

Linear OA(4¹⁹⁶, 550, F₄, 55) (dual of [550, 354, 56]-code), using 1 times code embedding in larger space based on linear OA(4¹⁹⁵, 549, F₄, 55) (dual of [549, 354, 56]-code), using

trace code [i] based on linear OA(64⁶⁵, 183, F₆₄, 55) (dual of [183, 118, 56]-code), using
- constructionÂ X applied to AG(F,120P) âŠ‚ AG(F,124P) [i] based on
  1. linear OA(64⁶², 176, F₆₄, 55) (dual of [176, 114, 56]-code), using algebraic-geometric code AG(F,120P) [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(64⁵⁸, 176, F₆₄, 51) (dual of [176, 118, 52]-code), using algebraic-geometric code AG(F,124P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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 OOA(4¹⁹⁶, 275, F₄, 2, 55) (dual of [(275, 2), 354, 56]-NRT-code)	[i]		OOA Folding