MinT - Information on Result #1299178

Information on Result #1299178

Linear OA(3¹⁹⁸, 235, F₃, 93) (dual of [235, 37, 94]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁹⁷, 233, F₃, 93) (dual of [233, 36, 94]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3¹⁸³, 215, F₃, 93) (dual of [215, 32, 94]-code), using
    - 29 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
        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]
        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]
        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]
  2. linear OA(3¹⁸³, 219, F₃, 85) (dual of [219, 36, 86]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸³Â > V_b^sâˆ’1(kâˆ’1)Â = 2007 475157 792492 760056 939638 399468 908859 093170 061955 968109 996071 488981 984494 532151 774953 [i]
  3. linear OA(3¹⁰, 14, F₃, 7) (dual of [14, 4, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰, 15, F₃, 7) (dual of [15, 5, 8]-code), using
      - 1 times truncation [i] based on linear OA(3¹¹, 16, F₃, 8) (dual of [16, 5, 9]-code), using
        an explicit generator matrix [i]
linear OA(3¹⁹⁷, 234, F₃, 92) (dual of [234, 37, 93]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁹⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 9617 633842 054166 101312 617030 056798 912102 275844 128621 184630 596110 842318 541965 230864 098438 282595 [i]
linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code) (see above)

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(3¹⁹⁹, 237, F₃, 93) (dual of [237, 38, 94]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound