MinT - Information on Result #2485551

Information on Result #2485551

Linear OOA(3¹⁰², 2391493, F₃, 2, 11) (dual of [(2391493, 2), 4782884, 12]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁰¹, 2391493, F₃, 2, 11) (dual of [(2391493, 2), 4782885, 12]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁰¹, 4782986, F₃, 11) (dual of [4782986, 4782885, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁰, 4782985, F₃, 11) (dual of [4782985, 4782885, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(9) [i] based on
    1. linear OA(3⁹⁹, 4782969, F₃, 11) (dual of [4782969, 4782870, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹⁵, 16, F₃, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
      - dual of repetition code with length 16 [i]
    4. linear OA(3¹, 16, F₃, 1) (dual of [16, 15, 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(3¹⁰², 1732503, F₃, 3, 11) (dual of [(1732503, 3), 5197407, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰², 1732503, F₃, 4, 11) (dual of [(1732503, 4), 6929910, 12]-NRT-code)	[i]
3	Linear OOA(3¹⁰², 1732503, F₃, 5, 11) (dual of [(1732503, 5), 8662413, 12]-NRT-code)	[i]
4	Digital (91, 102, 1732503)-net over F₃	[i]