MinT - Information on Result #906676

Information on Result #906676

Linear OOA(8²³, 406, F₈, 2, 7) (dual of [(406, 2), 789, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8¹, 73, F₈, 2, 1) (dual of [(73, 2), 145, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
  - Hamming code H(3,8) [i]
linear OOA(8⁵, 130, F₈, 2, 3) (dual of [(130, 2), 255, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
    - caps completed using a computer search [i]
linear OOA(8¹⁴, 130, F₈, 2, 7) (dual of [(130, 2), 246, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 7, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [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(8²³, 203, F₈, 3, 7) (dual of [(203, 3), 586, 8]-NRT-code)	[i]		OOA Folding