MinT - Information on Result #1521914

Information on Result #1521914

Linear OOA(3¹⁰¹, 3031, F₃, 3, 19) (dual of [(3031, 3), 8992, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰¹, 3031, F₃, 2, 19) (dual of [(3031, 2), 5961, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰¹, 3290, F₃, 2, 19) (dual of [(3290, 2), 6479, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰¹, 6580, F₃, 19) (dual of [6580, 6479, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰¹, 6581, F₃, 19) (dual of [6581, 6480, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
      1. linear OA(3⁹⁷, 6561, F₃, 19) (dual of [6561, 6464, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(3⁸¹, 6561, F₃, 16) (dual of [6561, 6480, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(3⁴, 20, F₃, 2) (dual of [20, 16, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹⁰¹, 1515, F₃, 5, 19) (dual of [(1515, 5), 7474, 20]-NRT-code)	[i]		OOA Folding