MinT - Information on Result #906652

Information on Result #906652

Linear OOA(8²⁴, 520, F₈, 2, 7) (dual of [(520, 2), 1016, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8⁰, 65, F₈, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁰, s, F₈, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(8¹, 65, F₈, 2, 1) (dual of [(65, 2), 129, 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(8¹, 65, F₈, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
linear OOA(8¹, 65, F₈, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
linear OOA(8¹, 65, F₈, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
linear OOA(8³, 65, F₈, 2, 2) (dual of [(65, 2), 127, 3]-NRT-code), using
- discarding factors / shortening the dual code based on 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(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
  - ovoid in PG(3,Â 8) [i]
linear OOA(8¹³, 65, F₈, 2, 7) (dual of [(65, 2), 117, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 65)-net over F₈, using
  - base reduction for projective spaces (embedding PG(6,64) in PG(12,8)) 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(8²⁴, 260, F₈, 3, 7) (dual of [(260, 3), 756, 8]-NRT-code)	[i]		OOA Folding