MinT - Information on Result #1016038

Information on Result #1016038

Linear OOA(9⁷¹, 1594361, F₉, 3, 11) (dual of [(1594361, 3), 4783012, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁷, 36, F₉, 3, 5) (dual of [(36, 3), 101, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
  - a code by Danev and Olsson [i]
linear OOA(9⁶⁴, 1594325, F₉, 3, 11) (dual of [(1594325, 3), 4782911, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁶⁴, 4782975, F₉, 11) (dual of [4782975, 4782911, 12]-code), using
  - discarding factors / shortening the dual code based on 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.

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		This result only	Method
1	Linear OOA(9⁷², 1594361, F₉, 3, 11) (dual of [(1594361, 3), 4783011, 12]-NRT-code)	[i]		OOA Duplication