MinT - Information on Result #938453

Information on Result #938453

Linear OOA(3¹⁴², 154, F₃, 2, 50) (dual of [(154, 2), 166, 51]-NRT-code), using trace code based on linear OOA(9⁷¹, 77, F₉, 2, 50) (dual of [(77, 2), 83, 51]-NRT-code), using

constructionÂ X applied to AG(2;F,95P) âŠ‚ AG(2;F,100P) [i] based on
1. linear OOA(9⁶⁷, 73, F₉, 2, 50) (dual of [(73, 2), 79, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,95P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(9⁶², 73, F₉, 2, 45) (dual of [(73, 2), 84, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,100P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
3. linear OOA(9⁴, 4, F₉, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁴, 9, F₉, 2, 4) (dual of [(9, 2), 14, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;14,9) [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(3¹⁴³, 154, F₃, 2, 50) (dual of [(154, 2), 165, 51]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁴², 77, F₃, 3, 50) (dual of [(77, 3), 89, 51]-NRT-code)	[i]	OOA Folding
3	Linear OOA(3¹⁴², 77, F₃, 4, 50) (dual of [(77, 4), 166, 51]-NRT-code)	[i]	OOA Folding