MinT - Information on Result #1298899

Information on Result #1298899

Linear OA(3¹⁷⁷, 210, F₃, 84) (dual of [210, 33, 85]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁷⁴, 206, F₃, 84) (dual of [206, 32, 85]-code), using
- 38 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(3¹⁷⁴, 207, F₃, 81) (dual of [207, 33, 82]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁷⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 57969 662298 850075 921507 641900 857889 503801 873617 000438 561035 717199 862035 457000 798841 [i]
linear OA(3², 3, F₃, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reedâ€“Solomon code RS(1,3) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁸⁰, 215, F₃, 84) (dual of [215, 35, 85]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound