MinT - Information on Result #1048433

Information on Result #1048433

Linear OOA(4¹⁷¹, 540, F₄, 3, 44) (dual of [(540, 3), 1449, 45]-NRT-code), using trace code based on linear OOA(64⁵⁷, 180, F₆₄, 3, 44) (dual of [(180, 3), 483, 45]-NRT-code), using

constructionÂ X applied to AG(3;F,483P) âŠ‚ AG(3;F,490P) [i] based on
1. linear OOA(64⁵¹, 176, F₆₄, 3, 44) (dual of [(176, 3), 477, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,483P) [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(64⁴⁴, 176, F₆₄, 3, 37) (dual of [(176, 3), 484, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,490P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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(4¹⁷², 540, F₄, 3, 44) (dual of [(540, 3), 1448, 45]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4¹⁷³, 540, F₄, 3, 44) (dual of [(540, 3), 1447, 45]-NRT-code)	[i]		OOA Duplication