MinT - Information on Result #2485690

Information on Result #2485690

Linear OOA(3¹⁰⁹, 797177, F₃, 2, 12) (dual of [(797177, 2), 1594245, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹⁰⁷, 797176, F₃, 2, 12) (dual of [(797176, 2), 1594245, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁰⁷, 1594352, F₃, 12) (dual of [1594352, 1594245, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁶, 1594351, F₃, 12) (dual of [1594351, 1594245, 13]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(9) [i] based on
    1. linear OA(3¹⁰⁵, 1594323, F₃, 13) (dual of [1594323, 1594218, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(3⁷⁹, 1594323, F₃, 10) (dual of [1594323, 1594244, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(3²⁷, 28, F₃, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
      - dual of repetition code with length 28 [i]
    4. linear OA(3¹, 28, F₃, 1) (dual of [28, 27, 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(3¹⁰⁹, 797177, F₃, 3, 12) (dual of [(797177, 3), 2391422, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰⁹, 797177, F₃, 4, 12) (dual of [(797177, 4), 3188599, 13]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁹, 797177, F₃, 5, 12) (dual of [(797177, 5), 3985776, 13]-NRT-code)	[i]
4	Digital (97, 109, 797177)-net over F₃	[i]