MinT - Information on Result #731934

Information on Result #731934

Linear OA(9⁷¹, 4783049, F₉, 11) (dual of [4783049, 4782978, 12]-code), using (u,Â u+v)-construction based on

linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
- a code by Danev and Olsson [i]
linear OA(9⁶⁴, 4782976, F₉, 11) (dual of [4782976, 4782912, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(9⁷², 4783050, F₉, 11) (dual of [4783050, 4782978, 12]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(9⁷¹, 4783049, F₉, 2, 11) (dual of [(4783049, 2), 9566027, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(9⁷¹, 4783049, F₉, 3, 11) (dual of [(4783049, 3), 14349076, 12]-NRT-code)	[i]
4	Digital (60, 71, 4783049)-net over F₉	[i]
5	Linear OOA(9⁷¹, 2391524, F₉, 2, 11) (dual of [(2391524, 2), 4782977, 12]-NRT-code)	[i]	OOA Folding
6	Linear OOA(9⁷¹, 1594349, F₉, 3, 11) (dual of [(1594349, 3), 4782976, 12]-NRT-code)	[i]	OOA Folding
7	Linear OOA(9⁷¹, 956609, F₉, 11, 11) (dual of [(956609, 11), 10522628, 12]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row