MinT - Information on Result #2672994

Information on Result #2672994

Linear OOA(2²⁵², 141, F₂, 3, 81) (dual of [(141, 3), 171, 82]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁴⁹, 140, F₂, 3, 81) (dual of [(140, 3), 171, 82]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴⁸, 35, F₈, 3, 40) (dual of [(35, 3), 57, 41]-NRT-code), using
  - extracting embedded OOA [i] based on digital (8, 48, 35)-net over F₈, using
    - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [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		This result only	Method
1	Linear OOA(2²⁵³, 141, F₂, 3, 81) (dual of [(141, 3), 170, 82]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁵⁴, 141, F₂, 3, 81) (dual of [(141, 3), 169, 82]-NRT-code)	[i]		OOA Duplication