MinT - Information on Result #1520320

Information on Result #1520320

Linear OOA(3³⁵, 3286, F₃, 3, 7) (dual of [(3286, 3), 9823, 8]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3³⁵, 3286, F₃, 2, 7) (dual of [(3286, 2), 6537, 8]-NRT-code), using

OOA 2-folding [i] based on linear OA(3³⁵, 6572, F₃, 7) (dual of [6572, 6537, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3³⁴, 6571, F₃, 7) (dual of [6571, 6537, 8]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
    1. linear OA(3³³, 6561, F₃, 7) (dual of [6561, 6528, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3²⁵, 6561, F₃, 5) (dual of [6561, 6536, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(3⁹, 10, F₃, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
      - dual of repetition code with length 10 [i]
    4. linear OA(3¹, 10, F₃, 1) (dual of [10, 9, 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(3³⁵, 3285, F₃, 4, 7) (dual of [(3285, 4), 13105, 8]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3³⁵, 3285, F₃, 5, 7) (dual of [(3285, 5), 16390, 8]-NRT-code)	[i]
3	Linear OOA(3³⁵, 3285, F₃, 9, 7) (dual of [(3285, 9), 29530, 8]-NRT-code)	[i]