MinT - Information on Result #731402

Information on Result #731402

Linear OA(9⁸⁴, 1062904, F₉, 14) (dual of [1062904, 1062820, 15]-code), using trace code based on linear OA(81⁴², 531452, F₈₁, 14) (dual of [531452, 531410, 15]-code), using

constructionÂ X applied to C_e(13) âŠ‚ C_e(10) [i] based on
1. linear OA(81⁴⁰, 531441, F₈₁, 14) (dual of [531441, 531401, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
2. linear OA(81³¹, 531441, F₈₁, 11) (dual of [531441, 531410, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
3. linear OA(81², 11, F₈₁, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), using
  - discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
    - Reedâ€“Solomon code RS(79,81) [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(9⁸⁴, 1062904, F₉, 2, 14) (dual of [(1062904, 2), 2125724, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(9⁸⁴, 1062904, F₉, 3, 14) (dual of [(1062904, 3), 3188628, 15]-NRT-code)	[i]
3	Digital (70, 84, 1062904)-net over F₉	[i]
4	Linear OOA(9⁸⁴, 531452, F₉, 2, 14) (dual of [(531452, 2), 1062820, 15]-NRT-code)	[i]	OOA Folding
5	Linear OOA(9⁸⁴, 354301, F₉, 3, 14) (dual of [(354301, 3), 1062819, 15]-NRT-code)	[i]	OOA Folding
6	Linear OOA(9⁸⁴, 151843, F₉, 14, 14) (dual of [(151843, 14), 2125718, 15]-NRT-code)	[i]	OA Folding and Stacking