MinT - Information on Result #1553561

Information on Result #1553561

Linear OOA(8¹³, 8066, F₈, 3, 4) (dual of [(8066, 3), 24185, 5]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8¹³, 8066, F₈, 4) (dual of [8066, 8053, 5]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
  - trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
    - 1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
      - a code by Danev and Olsson [i]
2. linear OA(8¹², 8065, F₈, 3) (dual of [8065, 8053, 4]-code or 8065-cap in PG(11,8)), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8¹²Â > V_b^sâˆ’1(kâˆ’1)Â = 1593 047233 [i]
3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: 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(8¹³, 8066, F₈, 4, 4) (dual of [(8066, 4), 32251, 5]-NRT-code)	[i]		Appending kth Column