MinT - Information on Result #812942

Information on Result #812942

Linear OOA(3¹⁰⁵, 797168, F₃, 2, 12) (dual of [(797168, 2), 1594231, 13]-NRT-code), using OOA 2-folding based on linear OA(3¹⁰⁵, 1594336, F₃, 12) (dual of [1594336, 1594231, 13]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁰⁵, 1594337, F₃, 12) (dual of [1594337, 1594232, 13]-code), using
- 1 times truncation [i] based on linear OA(3¹⁰⁶, 1594338, F₃, 13) (dual of [1594338, 1594232, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [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(3⁹², 1594323, F₃, 11) (dual of [1594323, 1594231, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(3¹⁴, 15, F₃, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
      - dual of repetition code with length 15 [i]
    4. linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 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(3¹⁰⁵, 598554, F₃, 3, 12) (dual of [(598554, 3), 1795557, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰⁵, 598554, F₃, 4, 12) (dual of [(598554, 4), 2394111, 13]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁵, 598554, F₃, 5, 12) (dual of [(598554, 5), 2992665, 13]-NRT-code)	[i]
4	Digital (93, 105, 598554)-net over F₃	[i]