MinT - Information on Result #1522317

Information on Result #1522317

Linear OOA(3¹¹¹, 9401, F₃, 3, 18) (dual of [(9401, 3), 28092, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹¹, 9401, F₃, 2, 18) (dual of [(9401, 2), 18691, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹¹¹, 9852, F₃, 2, 18) (dual of [(9852, 2), 19593, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹¹¹, 19704, F₃, 18) (dual of [19704, 19593, 19]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹¹⁰, 19703, F₃, 18) (dual of [19703, 19593, 19]-code), using
    - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(15) [i] based on
      1. linear OA(3¹⁰⁹, 19683, F₃, 19) (dual of [19683, 19574, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(3¹⁹, 20, F₃, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
        dual of repetition code with length 20 [i]
      4. linear OA(3¹, 20, F₃, 1) (dual of [20, 19, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: 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(3¹¹¹, 4700, F₃, 5, 18) (dual of [(4700, 5), 23389, 19]-NRT-code)	[i]		OOA Folding