MinT - Information on Result #735462

Information on Result #735462

Linear OA(81²⁸, 13044, F₈₁, 11) (dual of [13044, 13016, 12]-code), using (u,Â u+v)-construction based on

linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
- a code by Danev and Olsson [i]
linear OA(81²¹, 6563, F₈₁, 11) (dual of [6563, 6542, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(81²¹, 6561, F₈₁, 11) (dual of [6561, 6540, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(81¹⁹, 6561, F₈₁, 10) (dual of [6561, 6542, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81²⁸, 13044, F₈₁, 2, 11) (dual of [(13044, 2), 26060, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(81²⁸, 13044, F₈₁, 3, 11) (dual of [(13044, 3), 39104, 12]-NRT-code)	[i]
3	Linear OOA(81²⁸, 13044, F₈₁, 4, 11) (dual of [(13044, 4), 52148, 12]-NRT-code)	[i]
4	Digital (17, 28, 13044)-net over F₈₁	[i]
5	Linear OOA(81²⁸, 6522, F₈₁, 2, 11) (dual of [(6522, 2), 13016, 12]-NRT-code)	[i]	OOA Folding
6	Linear OOA(81²⁸, 4348, F₈₁, 3, 11) (dual of [(4348, 3), 13016, 12]-NRT-code)	[i]
7	Linear OOA(81²⁸, 3261, F₈₁, 4, 11) (dual of [(3261, 4), 13016, 12]-NRT-code)	[i]