MinT - Information on Result #1048514

Information on Result #1048514

Linear OOA(4²³¹, 546, F₄, 3, 61) (dual of [(546, 3), 1407, 62]-NRT-code), using trace code based on linear OOA(64⁷⁷, 182, F₆₄, 3, 61) (dual of [(182, 3), 469, 62]-NRT-code), using

constructionÂ X applied to AG(3;F,466P) âŠ‚ AG(3;F,476P) [i] based on
1. linear OOA(64⁶⁸, 176, F₆₄, 3, 61) (dual of [(176, 3), 460, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,466P) [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(64⁹, 6, F₆₄, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁹, 64, F₆₄, 3, 9) (dual of [(64, 3), 183, 10]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;183,64) [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(4²³², 546, F₄, 3, 61) (dual of [(546, 3), 1406, 62]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²³³, 546, F₄, 3, 61) (dual of [(546, 3), 1405, 62]-NRT-code)	[i]		OOA Duplication