MinT - Information on Result #1298964

Information on Result #1298964

Linear OA(3¹⁸⁷, 220, F₃, 91) (dual of [220, 33, 92]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁸¹, 213, F₃, 91) (dual of [213, 32, 92]-code), using
- 31 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(3¹⁸¹, 214, F₃, 85) (dual of [214, 33, 86]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸¹Â > V_b^sâˆ’1(kâˆ’1)Â = 174 008132 274775 633679 311132 226037 579802 499509 180900 015176 809274 235439 835616 318219 208627 [i]
linear OA(3⁵, 6, F₃, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,3)), using
- dual of repetition code with length 6 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁸⁷, 220, F₃, 90) (dual of [220, 33, 91]-code)	[i]		Strength Reduction
2	Linear OA(3¹⁸⁵, 218, F₃, 89) (dual of [218, 33, 90]-code)	[i]		Truncation