MinT - Information on Result #1075487

Information on Result #1075487

Linear OOA(2²²⁴, 112, F₂, 4, 79) (dual of [(112, 4), 224, 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, 4, 78) (dual of [(112, 4), 224, 79]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁸, 113, F₂, 4, 79) (dual of [(113, 4), 224, 80]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(2²³², 114, F₂, 4, 79) (dual of [(114, 4), 224, 80]-NRT-code)	[i]
4	Linear OOA(2²³⁶, 115, F₂, 4, 79) (dual of [(115, 4), 224, 80]-NRT-code)	[i]
5	Linear OOA(2²⁴⁰, 116, F₂, 4, 79) (dual of [(116, 4), 224, 80]-NRT-code)	[i]
6	Linear OOA(2²⁴⁴, 117, F₂, 4, 79) (dual of [(117, 4), 224, 80]-NRT-code)	[i]
7	Linear OOA(2²⁴⁸, 118, F₂, 4, 79) (dual of [(118, 4), 224, 80]-NRT-code)	[i]
8	Linear OOA(2²⁵², 119, F₂, 4, 79) (dual of [(119, 4), 224, 80]-NRT-code)	[i]
9	Linear OOA(2²²⁵, 112, F₂, 4, 79) (dual of [(112, 4), 223, 80]-NRT-code)	[i]		OOA Duplication
10	Linear OOA(2²²⁷, 112, F₂, 4, 79) (dual of [(112, 4), 221, 80]-NRT-code)	[i]		OOA Duplication
11	Linear OOA(2²²⁴, 56, F₂, 7, 79) (dual of [(56, 7), 168, 80]-NRT-code)	[i]		OOA Folding
12	Linear OOA(2²²⁴, 56, F₂, 8, 79) (dual of [(56, 8), 224, 80]-NRT-code)	[i]		OOA Folding