MinT - Information on Result #1299594

Information on Result #1299594

Linear OA(3²³⁷, 276, F₃, 113) (dual of [276, 39, 114]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3²³³, 270, F₃, 113) (dual of [270, 37, 114]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3²⁰³, 235, F₃, 113) (dual of [235, 32, 114]-code), using
    - 9 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(3²⁰³, 240, F₃, 95) (dual of [240, 37, 96]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3²⁰³Â > V_b^sâˆ’1(kâˆ’1)Â = 5 636210 405882 976919 092173 276836 321771 902726 578845 461098 035433 727009 624671 086292 827162 301503 803115 [i]
  3. linear OA(3²⁵, 30, F₃, 17) (dual of [30, 5, 18]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
        projective code from ovoid in PG(3,Â 3) [i]
      2. linear OA(3⁹, 10, F₃, 8) (dual of [10, 1, 9]-code), using
        strength reduction [i] based on linear OA(3⁹, 10, F₃, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
        dual of repetition code with length 10 [i]
      3. linear OA(3¹⁰, 10, F₃, 10) (dual of [10, 0, 11]-code or 10-arc in PG(9,3)), using
        complete OA / dual of code with only one code word [i]
linear OA(3²³³, 272, F₃, 110) (dual of [272, 39, 111]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3²³³Â > V_b^sâˆ’1(kâˆ’1)Â = 987 798044 299078 202334 459303 752870 209414 718267 191554 983333 503131 489977 082006 005415 413413 443428 256718 859068 305003 [i]
linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reedâ€“Solomon code RS_e(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [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(3²³⁸, 278, F₃, 113) (dual of [278, 40, 114]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound