MinT - Information on Result #731896

Information on Result #731896

Linear OA(8⁷¹, 2097216, F₈, 11) (dual of [2097216, 2097145, 12]-code), using (u,Â u+v)-construction based on

linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
- a code by Danev and Olsson [i]
linear OA(8⁶⁴, 2097159, F₈, 11) (dual of [2097159, 2097095, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(8⁶⁴, 2097152, F₈, 11) (dual of [2097152, 2097088, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(8⁵⁷, 2097152, F₈, 10) (dual of [2097152, 2097095, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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 OOA(8⁷¹, 2097216, F₈, 2, 11) (dual of [(2097216, 2), 4194361, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(8⁷¹, 2097216, F₈, 3, 11) (dual of [(2097216, 3), 6291577, 12]-NRT-code)	[i]
3	Digital (60, 71, 2097216)-net over F₈	[i]
4	Linear OOA(8⁷¹, 1048608, F₈, 2, 11) (dual of [(1048608, 2), 2097145, 12]-NRT-code)	[i]	OOA Folding
5	Linear OOA(8⁷¹, 699072, F₈, 3, 11) (dual of [(699072, 3), 2097145, 12]-NRT-code)	[i]	OOA Folding
6	Linear OOA(8⁷¹, 419443, F₈, 11, 11) (dual of [(419443, 11), 4613802, 12]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row