MinT - Information on Result #1414081

Information on Result #1414081

Linear OOA(3¹⁹⁰, 2250, F₃, 2, 38) (dual of [(2250, 2), 4310, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁹⁰, 2250, F₃, 38) (dual of [2250, 2060, 39]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁹⁰, 2272, F₃, 38) (dual of [2272, 2082, 39]-code), using
- 64 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0, 1, 16 times 0) [i] based on linear OA(3¹⁷⁶, 2194, F₃, 38) (dual of [2194, 2018, 39]-code), using
  - constructionÂ X applied to C_e(37) âŠ‚ C_e(36) [i] based on
    1. linear OA(3¹⁷⁶, 2187, F₃, 38) (dual of [2187, 2011, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
    2. linear OA(3¹⁶⁹, 2187, F₃, 37) (dual of [2187, 2018, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    3. linear OA(3⁰, 7, F₃, 0) (dual of [7, 7, 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(3¹⁹⁰, 1125, F₃, 3, 38) (dual of [(1125, 3), 3185, 39]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁹⁰, 1125, F₃, 4, 38) (dual of [(1125, 4), 4310, 39]-NRT-code)	[i]		OOA Folding