MinT - Information on Result #2428874

Information on Result #2428874

Linear OOA(2²⁵¹, 184, F₂, 2, 86) (dual of [(184, 2), 117, 87]-NRT-code), using strength reduction based on linear OOA(2²⁵¹, 184, F₂, 2, 87) (dual of [(184, 2), 117, 88]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁵³, 46, F₈, 2, 43) (dual of [(46, 2), 39, 44]-NRT-code), using
  - extracting embedded OOA [i] based on digital (10, 53, 46)-net over F₈, using
    - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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(2²⁵³, 185, F₂, 2, 86) (dual of [(185, 2), 117, 87]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵², 184, F₂, 2, 86) (dual of [(184, 2), 116, 87]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵¹, 92, F₂, 4, 86) (dual of [(92, 4), 117, 87]-NRT-code)	[i]	OOA Folding