MinT - Information on Result #1607968

Information on Result #1607968

Linear OOA(3¹⁹², 7771, F₃, 4, 32) (dual of [(7771, 4), 30892, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹², 7771, F₃, 2, 32) (dual of [(7771, 2), 15350, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹², 9847, F₃, 2, 32) (dual of [(9847, 2), 19502, 33]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁹⁰, 9846, F₃, 2, 32) (dual of [(9846, 2), 19502, 33]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁹⁰, 19692, F₃, 32) (dual of [19692, 19502, 33]-code), using
    - constructionÂ X applied to C_e(31) âŠ‚ C_e(30) [i] based on
      1. linear OA(3¹⁹⁰, 19683, F₃, 32) (dual of [19683, 19493, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
      2. linear OA(3¹⁸¹, 19683, F₃, 31) (dual of [19683, 19502, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      3. linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3¹⁹², 1942, F₃, 36, 32) (dual of [(1942, 36), 69720, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row