MinT - Information on Result #1048560

Information on Result #1048560

Linear OOA(4²⁴⁹, 552, F₄, 3, 64) (dual of [(552, 3), 1407, 65]-NRT-code), using trace code based on linear OOA(64⁸³, 184, F₆₄, 3, 64) (dual of [(184, 3), 469, 65]-NRT-code), using

constructionÂ X applied to AG(3;F,463P) âŠ‚ AG(3;F,476P) [i] based on
1. linear OOA(64⁷¹, 176, F₆₄, 3, 64) (dual of [(176, 3), 457, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,463P) [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 OOA(64⁵⁸, 176, F₆₄, 3, 51) (dual of [(176, 3), 470, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,476P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹², 8, F₆₄, 3, 12) (dual of [(8, 3), 12, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹², 64, F₆₄, 3, 12) (dual of [(64, 3), 180, 13]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;180,64) [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, 552, F₄, 3, 64) (dual of [(552, 3), 1406, 65]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²⁵¹, 552, F₄, 3, 64) (dual of [(552, 3), 1405, 65]-NRT-code)	[i]		OOA Duplication