MinT - Information on Result #1048457

Information on Result #1048457

Linear OOA(4¹⁹⁵, 543, F₄, 3, 51) (dual of [(543, 3), 1434, 52]-NRT-code), using trace code based on linear OOA(64⁶⁵, 181, F₆₄, 3, 51) (dual of [(181, 3), 478, 52]-NRT-code), using

constructionÂ X applied to AG(3;F,476P) âŠ‚ AG(3;F,484P) [i] based on
1. 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, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64⁵⁰, 176, F₆₄, 3, 43) (dual of [(176, 3), 478, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,484P) [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(4¹⁹⁸, 544, F₄, 3, 51) (dual of [(544, 3), 1434, 52]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁹⁶, 543, F₄, 3, 51) (dual of [(543, 3), 1433, 52]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4¹⁹⁷, 543, F₄, 3, 51) (dual of [(543, 3), 1432, 52]-NRT-code)	[i]	OOA Duplication