MinT - Information on Result #1048496

Information on Result #1048496

Linear OOA(4²¹⁹, 537, F₄, 3, 62) (dual of [(537, 3), 1392, 63]-NRT-code), using trace code based on linear OOA(64⁷³, 179, F₆₄, 3, 62) (dual of [(179, 3), 464, 63]-NRT-code), using

constructionÂ X applied to AG(3;F,465P) âŠ‚ AG(3;F,470P) [i] based on
1. linear OOA(64⁶⁹, 176, F₆₄, 3, 62) (dual of [(176, 3), 459, 63]-NRT-code), using algebraic-geometric NRT-code AG(3;F,465P) [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(64⁶⁴, 176, F₆₄, 3, 57) (dual of [(176, 3), 464, 58]-NRT-code), using algebraic-geometric NRT-code AG(3;F,470P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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		Method
1	Linear OOA(4²²², 538, F₄, 3, 62) (dual of [(538, 3), 1392, 63]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4²²⁰, 537, F₄, 3, 62) (dual of [(537, 3), 1391, 63]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4²²¹, 537, F₄, 3, 62) (dual of [(537, 3), 1390, 63]-NRT-code)	[i]	OOA Duplication