MinT - Information on Result #876615

Information on Result #876615

Linear OOA(81⁵², 265722, F₈₁, 2, 18) (dual of [(265722, 2), 531392, 19]-NRT-code), using OOA 2-folding based on linear OA(81⁵², 531444, F₈₁, 18) (dual of [531444, 531392, 19]-code), using

constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
1. linear OA(81⁵², 531441, F₈₁, 18) (dual of [531441, 531389, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
2. linear OA(81⁴⁹, 531441, F₈₁, 17) (dual of [531441, 531392, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [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(81⁶¹, 265804, F₈₁, 2, 18) (dual of [(265804, 2), 531547, 19]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁶², 265822, F₈₁, 2, 18) (dual of [(265822, 2), 531582, 19]-NRT-code)	[i]
3	Linear OOA(81⁶³, 265838, F₈₁, 2, 18) (dual of [(265838, 2), 531613, 19]-NRT-code)	[i]
4	Linear OOA(81⁶⁵, 265886, F₈₁, 2, 18) (dual of [(265886, 2), 531707, 19]-NRT-code)	[i]
5	Linear OOA(81⁶⁶, 265904, F₈₁, 2, 18) (dual of [(265904, 2), 531742, 19]-NRT-code)	[i]
6	Linear OOA(81⁶⁷, 265922, F₈₁, 2, 18) (dual of [(265922, 2), 531777, 19]-NRT-code)	[i]
7	Linear OOA(81⁶⁸, 265938, F₈₁, 2, 18) (dual of [(265938, 2), 531808, 19]-NRT-code)	[i]
8	Linear OOA(81⁶⁸, 265968, F₈₁, 2, 18) (dual of [(265968, 2), 531868, 19]-NRT-code)	[i]
9	Linear OOA(81⁵², 184620, F₈₁, 3, 18) (dual of [(184620, 3), 553808, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
10	Linear OOA(81⁵², 184620, F₈₁, 4, 18) (dual of [(184620, 4), 738428, 19]-NRT-code)	[i]
11	Digital (34, 52, 184620)-net over F₈₁	[i]