MinT - Information on Result #1298944

Information on Result #1298944

Linear OA(3¹⁸⁴, 217, F₃, 89) (dual of [217, 33, 90]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁷⁹, 211, F₃, 89) (dual of [211, 32, 90]-code), using
- 33 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(3¹⁷⁹, 212, F₃, 84) (dual of [212, 33, 85]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁷⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 20 836196 073517 781678 121052 821271 546066 313319 772523 301112 629442 256912 604801 557599 863003 [i]
linear OA(3⁴, 5, F₃, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,3)), using
- dual of repetition code with length 5 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁸⁴, 217, F₃, 88) (dual of [217, 33, 89]-code)	[i]		Strength Reduction
2	Linear OA(3¹⁸², 215, F₃, 87) (dual of [215, 33, 88]-code)	[i]		Truncation