MinT - Information on Result #1047741

Information on Result #1047741

Linear OOA(2¹⁷⁶, 116, F₂, 3, 51) (dual of [(116, 3), 172, 52]-NRT-code), using trace code based on linear OOA(4⁸⁸, 58, F₄, 3, 51) (dual of [(58, 3), 86, 52]-NRT-code), using

constructionÂ X applied to AG(3;F,113P) âŠ‚ AG(3;F,118P) [i] based on
1. linear OOA(4⁸⁴, 55, F₄, 3, 51) (dual of [(55, 3), 81, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,113P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4⁷⁹, 55, F₄, 3, 46) (dual of [(55, 3), 86, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,118P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,4) [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(2¹⁷⁶, 116, F₂, 3, 50) (dual of [(116, 3), 172, 51]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁹, 117, F₂, 3, 51) (dual of [(117, 3), 172, 52]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2¹⁷⁷, 116, F₂, 3, 51) (dual of [(116, 3), 171, 52]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁷⁶, 58, F₂, 5, 51) (dual of [(58, 5), 114, 52]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2¹⁷⁶, 58, F₂, 6, 51) (dual of [(58, 6), 172, 52]-NRT-code)	[i]	OOA Folding