MinT - Information on Result #1452991

Information on Result #1452991

Linear OOA(16¹³, 130562, F₁₆, 2, 4) (dual of [(130562, 2), 261111, 5]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16¹³, 130562, F₁₆, 4) (dual of [130562, 130549, 5]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(16¹², 130560, F₁₆, 4) (dual of [130560, 130548, 5]-code), using
  - trace code [i] based on linear OA(256⁶, 65280, F₂₅₆, 4) (dual of [65280, 65274, 5]-code), using
    - 1 times truncation [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [i]
2. linear OA(16¹², 130561, F₁₆, 3) (dual of [130561, 130549, 4]-code or 130561-cap in PG(11,16)), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16¹²Â > V_b^sâˆ’1(kâˆ’1)Â = 1 917652 550401 [i]
3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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(16¹³, 130561, F₁₆, 6, 4) (dual of [(130561, 6), 783353, 5]-NRT-code)	[i]		OOA Stacking with Additional Row