MinT - Information on Result #938461

Information on Result #938461

Linear OOA(3¹⁴⁴, 154, F₃, 2, 51) (dual of [(154, 2), 164, 52]-NRT-code), using trace code based on linear OOA(9⁷², 77, F₉, 2, 51) (dual of [(77, 2), 82, 52]-NRT-code), using

constructionÂ X applied to AG(2;F,94P) âŠ‚ AG(2;F,99P) [i] based on
1. linear OOA(9⁶⁸, 73, F₉, 2, 51) (dual of [(73, 2), 78, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,94P) [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(9⁶³, 73, F₉, 2, 46) (dual of [(73, 2), 83, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,99P) [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(3¹⁴⁵, 154, F₃, 2, 51) (dual of [(154, 2), 163, 52]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁴⁴, 77, F₃, 3, 51) (dual of [(77, 3), 87, 52]-NRT-code)	[i]	OOA Folding
3	Linear OOA(3¹⁴⁴, 77, F₃, 4, 51) (dual of [(77, 4), 164, 52]-NRT-code)	[i]	OOA Folding