MinT - Information on Result #1110975

Information on Result #1110975

Linear OOA(2²²⁴, 112, F₂, 5, 79) (dual of [(112, 5), 336, 80]-NRT-code), using extracting embedded OOA based on digital (145, 224, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 112, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [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]

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		This result only	Method
1	Linear OOA(2²²⁴, 112, F₂, 5, 78) (dual of [(112, 5), 336, 79]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁴, 112, F₂, 5, 77) (dual of [(112, 5), 336, 78]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2²²⁹, 113, F₂, 5, 79) (dual of [(113, 5), 336, 80]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(2²³⁴, 114, F₂, 5, 79) (dual of [(114, 5), 336, 80]-NRT-code)	[i]
5	Linear OOA(2²³⁹, 115, F₂, 5, 79) (dual of [(115, 5), 336, 80]-NRT-code)	[i]
6	Linear OOA(2²⁴⁴, 116, F₂, 5, 79) (dual of [(116, 5), 336, 80]-NRT-code)	[i]
7	Linear OOA(2²⁴⁹, 117, F₂, 5, 79) (dual of [(117, 5), 336, 80]-NRT-code)	[i]
8	Linear OOA(2²⁵⁴, 118, F₂, 5, 79) (dual of [(118, 5), 336, 80]-NRT-code)	[i]
9	Linear OOA(2²²⁵, 112, F₂, 5, 79) (dual of [(112, 5), 335, 80]-NRT-code)	[i]		OOA Duplication
10	Linear OOA(2²²⁷, 112, F₂, 5, 79) (dual of [(112, 5), 333, 80]-NRT-code)	[i]		OOA Duplication