MinT - Information on Result #731043

Information on Result #731043

Linear OA(7⁶⁶, 4806, F₇, 17) (dual of [4806, 4740, 18]-code), using trace code based on linear OA(49³³, 2403, F₄₉, 17) (dual of [2403, 2370, 18]-code), using

constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
1. linear OA(49³³, 2401, F₄₉, 17) (dual of [2401, 2368, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
2. linear OA(49³¹, 2401, F₄₉, 16) (dual of [2401, 2370, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
3. linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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 OA(7⁶⁷, 4807, F₇, 17) (dual of [4807, 4740, 18]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(7⁶⁶, 4806, F₇, 2, 17) (dual of [(4806, 2), 9546, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(7⁶⁶, 4806, F₇, 3, 17) (dual of [(4806, 3), 14352, 18]-NRT-code)	[i]
4	Digital (49, 66, 4806)-net over F₇	[i]
5	Linear OA(7⁶⁷, 4816, F₇, 17) (dual of [4816, 4749, 18]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
6	Linear OA(7⁶⁸, 4879, F₇, 17) (dual of [4879, 4811, 18]-code)	[i]
7	Linear OA(7⁶⁹, 5139, F₇, 17) (dual of [5139, 5070, 18]-code)	[i]
8	Linear OA(7⁶⁷, 4808, F₇, 17) (dual of [4808, 4741, 18]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
9	Linear OOA(7⁶⁶, 2403, F₇, 2, 17) (dual of [(2403, 2), 4740, 18]-NRT-code)	[i]	OOA Folding
10	Linear OOA(7⁶⁶, 1602, F₇, 3, 17) (dual of [(1602, 3), 4740, 18]-NRT-code)	[i]	OOA Folding