MinT - Information on Result #1299084

Information on Result #1299084

Linear OA(3²¹⁰, 246, F₃, 101) (dual of [246, 36, 102]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁹¹, 223, F₃, 101) (dual of [223, 32, 102]-code), using
- 21 times truncation [i] based on linear OA(3²¹², 244, F₃, 122) (dual of [244, 32, 123]-code), using
  - constructionÂ X applied to C_e(121) âŠ‚ C_e(120) [i] based on
    1. linear OA(3²¹², 243, F₃, 122) (dual of [243, 31, 123]-code), using an extension C_e(121) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,121], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 122 [i]
    2. linear OA(3²¹¹, 243, F₃, 121) (dual of [243, 32, 122]-code), using an extension C_e(120) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,120], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 121 [i]
    3. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OA(3¹⁹¹, 227, F₃, 89) (dual of [227, 36, 90]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 10 005910 074425 938303 954249 028812 217220 479998 786434 234800 917779 895987 159045 412086 756658 553225 [i]
linear OA(3¹⁵, 19, F₃, 11) (dual of [19, 4, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using
  - residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [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 OA(3²⁰⁸, 244, F₃, 99) (dual of [244, 36, 100]-code)	[i]		Truncation
2	Linear OA(3²¹⁴, 252, F₃, 101) (dual of [252, 38, 102]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound