MinT - Information on Result #2690703

Information on Result #2690703

Linear OOA(4²⁴⁹, 1546, F₄, 3, 50) (dual of [(1546, 3), 4389, 51]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²⁴⁶, 1545, F₄, 3, 50) (dual of [(1545, 3), 4389, 51]-NRT-code), using

trace code [i] based on linear OOA(64⁸², 515, F₆₄, 3, 50) (dual of [(515, 3), 1463, 51]-NRT-code), using
- constructionÂ X applied to AG(3;F,1485P) âŠ‚ AG(3;F,1490P) [i] based on
  1. linear OOA(64⁷⁸, 512, F₆₄, 3, 50) (dual of [(512, 3), 1458, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1485P) [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 OOA(64⁷³, 512, F₆₄, 3, 45) (dual of [(512, 3), 1463, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1490P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;188,64) [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(4²⁵⁰, 1546, F₄, 3, 50) (dual of [(1546, 3), 4388, 51]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²⁵¹, 1546, F₄, 3, 50) (dual of [(1546, 3), 4387, 51]-NRT-code)	[i]		OOA Duplication