MinT - Information on Result #664554

Information on Result #664554

Linear OA(16²², 1179137, F₁₆, 5) (dual of [1179137, 1179115, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 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]
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
- Hamming code H(5,16) [i]
linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
  - a code by Danev and Olsson [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		Method
1	Linear OOA(16²², 1179137, F₁₆, 2, 5) (dual of [(1179137, 2), 2358252, 6]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (17, 22, 1179137)-net over F₁₆	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(16²², 589568, F₁₆, 2, 5) (dual of [(589568, 2), 1179114, 6]-NRT-code)	[i]	OOA Folding