MinT - Information on Result #731871

Information on Result #731871

Linear OA(7⁸⁰, 5764852, F₇, 11) (dual of [5764852, 5764772, 12]-code), using (u,Â u+v)-construction based on

linear OA(7⁷, 43, F₇, 5) (dual of [43, 36, 6]-code), using
- a code by Danev and Olsson [i]
linear OA(7⁷³, 5764809, F₇, 11) (dual of [5764809, 5764736, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(7⁷³, 5764801, F₇, 11) (dual of [5764801, 5764728, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(7⁶⁵, 5764801, F₇, 10) (dual of [5764801, 5764736, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(7⁰, 8, F₇, 0) (dual of [8, 8, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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(7⁸⁰, 5764852, F₇, 2, 11) (dual of [(5764852, 2), 11529624, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(7⁸⁰, 5764852, F₇, 3, 11) (dual of [(5764852, 3), 17294476, 12]-NRT-code)	[i]
3	Digital (69, 80, 5764852)-net over F₇	[i]
4	Linear OOA(7⁸⁰, 2882426, F₇, 2, 11) (dual of [(2882426, 2), 5764772, 12]-NRT-code)	[i]	OOA Folding
5	Linear OOA(7⁸⁰, 1921617, F₇, 3, 11) (dual of [(1921617, 3), 5764771, 12]-NRT-code)	[i]	OOA Folding
6	Linear OOA(7⁸⁰, 1152970, F₇, 11, 11) (dual of [(1152970, 11), 12682590, 12]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row