MinT - Information on Result #2283814

Information on Result #2283814

Linear OA(9⁸⁷, 4782986, F₉, 14) (dual of [4782986, 4782899, 15]-code), using 1 times code embedding in larger space based on linear OA(9⁸⁶, 4782985, F₉, 14) (dual of [4782985, 4782899, 15]-code), using

constructionÂ X4 applied to C_e(13) âŠ‚ C_e(11) [i] based on
1. linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
2. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
3. linear OA(9¹⁵, 16, F₉, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,9)), using
  - dual of repetition code with length 16 [i]
4. linear OA(9¹, 16, F₉, 1) (dual of [16, 15, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹, 728, F₉, 1) (dual of [728, 727, 2]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 9³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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(9⁸⁷, 4560461, F₉, 2, 14) (dual of [(4560461, 2), 9120835, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(9⁸⁷, 4560461, F₉, 3, 14) (dual of [(4560461, 3), 13681296, 15]-NRT-code)	[i]
3	Digital (73, 87, 4560461)-net over F₉	[i]
4	Linear OOA(9⁸⁷, 2391493, F₉, 2, 14) (dual of [(2391493, 2), 4782899, 15]-NRT-code)	[i]	OOA Folding