MinT - Information on Result #1048510

Information on Result #1048510

Linear OOA(4²²⁸, 543, F₄, 3, 62) (dual of [(543, 3), 1401, 63]-NRT-code), using trace code based on linear OOA(64⁷⁶, 181, F₆₄, 3, 62) (dual of [(181, 3), 467, 63]-NRT-code), using

constructionÂ X applied to AG(3;F,465P) âŠ‚ AG(3;F,473P) [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(64⁶¹, 176, F₆₄, 3, 54) (dual of [(176, 3), 467, 55]-NRT-code), using algebraic-geometric NRT-code AG(3;F,473P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁷, 5, F₆₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 3, 7) (dual of [(64, 3), 185, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;185,64) [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(4²³¹, 544, F₄, 3, 62) (dual of [(544, 3), 1401, 63]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4²²⁹, 543, F₄, 3, 62) (dual of [(543, 3), 1400, 63]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4²³⁰, 543, F₄, 3, 62) (dual of [(543, 3), 1399, 63]-NRT-code)	[i]	OOA Duplication