MinT - Information on Result #1008751

Information on Result #1008751

Linear OOA(3²²⁶, 3188650, F₃, 3, 18) (dual of [(3188650, 3), 9565724, 19]-NRT-code), using trace code based on linear OOA(9¹¹³, 1594325, F₉, 3, 18) (dual of [(1594325, 3), 4782862, 19]-NRT-code), using

OOA 3-folding [i] based on linear OA(9¹¹³, 4782975, F₉, 18) (dual of [4782975, 4782862, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹³, 4782976, F₉, 18) (dual of [4782976, 4782863, 19]-code), using
  - 1 times truncation [i] based on linear OA(9¹¹⁴, 4782977, F₉, 19) (dual of [4782977, 4782863, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(9¹⁰⁶, 4782969, F₉, 17) (dual of [4782969, 4782863, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(9¹, 8, F₉, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3²²⁷, 3188650, F₃, 3, 18) (dual of [(3188650, 3), 9565723, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²⁶, 1062883, F₃, 21, 18) (dual of [(1062883, 21), 22320317, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row