MinT - Information on Result #2485691

Information on Result #2485691

Linear OOA(3¹¹⁶, 2391500, F₃, 2, 12) (dual of [(2391500, 2), 4782884, 13]-NRT-code), using 3¹ times duplication based on linear OOA(3¹¹⁵, 2391500, F₃, 2, 12) (dual of [(2391500, 2), 4782885, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹¹⁵, 4783000, F₃, 12) (dual of [4783000, 4782885, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹¹⁴, 4782999, F₃, 12) (dual of [4782999, 4782885, 13]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(9) [i] based on
    1. linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(3⁸⁵, 4782969, F₃, 10) (dual of [4782969, 4782884, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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: Constructive and 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		Method
1	Linear OOA(3¹¹⁶, 2292218, F₃, 3, 12) (dual of [(2292218, 3), 6876538, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁶, 2292218, F₃, 4, 12) (dual of [(2292218, 4), 9168756, 13]-NRT-code)	[i]
3	Linear OOA(3¹¹⁶, 2292218, F₃, 5, 12) (dual of [(2292218, 5), 11460974, 13]-NRT-code)	[i]
4	Digital (104, 116, 2292218)-net over F₃	[i]