MinT - Information on Result #1644307

Information on Result #1644307

Linear OOA(3¹⁴⁴, 1594334, F₃, 5, 15) (dual of [(1594334, 5), 7971526, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁴, 1594334, F₃, 3, 15) (dual of [(1594334, 3), 4782858, 16]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁴⁴, 4783002, F₃, 15) (dual of [4783002, 4782858, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3¹⁴², 4783000, F₃, 15) (dual of [4783000, 4782858, 16]-code), using
  - constructionÂ X4 applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(3¹⁴¹, 4782970, F₃, 15) (dual of [4782970, 4782829, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(3¹¹³, 4782970, F₃, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    3. linear OA(3²⁹, 30, F₃, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
      - dual of repetition code with length 30 [i]
    4. linear OA(3¹, 30, F₃, 1) (dual of [30, 29, 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(3¹⁴⁵, 1594334, F₃, 5, 15) (dual of [(1594334, 5), 7971525, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁴⁶, 1594334, F₃, 5, 15) (dual of [(1594334, 5), 7971524, 16]-NRT-code)	[i]		OOA Duplication