MinT - Information on Result #1110839

Information on Result #1110839

Linear OOA(2¹⁹², 112, F₂, 5, 63) (dual of [(112, 5), 368, 64]-NRT-code), using extracting embedded OOA based on digital (129, 192, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 96, 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(2¹⁹², 112, F₂, 5, 62) (dual of [(112, 5), 368, 63]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁹², 112, F₂, 5, 61) (dual of [(112, 5), 368, 62]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2¹⁹⁷, 113, F₂, 5, 63) (dual of [(113, 5), 368, 64]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(2²⁰², 114, F₂, 5, 63) (dual of [(114, 5), 368, 64]-NRT-code)	[i]
5	Linear OOA(2²⁰⁷, 115, F₂, 5, 63) (dual of [(115, 5), 368, 64]-NRT-code)	[i]
6	Linear OOA(2²¹², 116, F₂, 5, 63) (dual of [(116, 5), 368, 64]-NRT-code)	[i]
7	Linear OOA(2¹⁹³, 112, F₂, 5, 63) (dual of [(112, 5), 367, 64]-NRT-code)	[i]		OOA Duplication
8	Linear OOA(2¹⁹⁵, 112, F₂, 5, 63) (dual of [(112, 5), 365, 64]-NRT-code)	[i]		OOA Duplication