MinT - Information on Result #1299041

Information on Result #1299041

Linear OA(3¹⁹⁸, 231, F₃, 98) (dual of [231, 33, 99]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁸⁸, 220, F₃, 98) (dual of [220, 32, 99]-code), using
- 24 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(3¹⁸⁸, 221, F₃, 88) (dual of [221, 33, 89]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 166226 581384 108144 629760 999433 110445 354823 581383 188210 726686 980266 459613 162567 126186 264113 [i]
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]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁹⁸, 231, F₃, 97) (dual of [231, 33, 98]-code)	[i]		Strength Reduction
2	Linear OA(3²⁰⁹, 247, F₃, 98) (dual of [247, 38, 99]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound