MinT - Information on Result #1048557

Information on Result #1048557

Linear OOA(4²⁴⁹, 1548, F₄, 3, 49) (dual of [(1548, 3), 4395, 50]-NRT-code), using trace code based on linear OOA(64⁸³, 516, F₆₄, 3, 49) (dual of [(516, 3), 1465, 50]-NRT-code), using

constructionÂ X applied to AG(3;F,1486P) âŠ‚ AG(3;F,1493P) [i] based on
1. linear OOA(64⁷⁷, 512, F₆₄, 3, 49) (dual of [(512, 3), 1459, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1486P) [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(64⁷⁰, 512, F₆₄, 3, 42) (dual of [(512, 3), 1466, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1493P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁶, 4, F₆₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 3, 6) (dual of [(64, 3), 186, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;186,64) [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, 1548, F₄, 3, 49) (dual of [(1548, 3), 4394, 50]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²⁵¹, 1548, F₄, 3, 49) (dual of [(1548, 3), 4393, 50]-NRT-code)	[i]		OOA Duplication