MinT - Information on Result #1299031

Information on Result #1299031

Linear OA(3¹⁹⁶, 229, F₃, 97) (dual of [229, 33, 98]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁸⁷, 219, F₃, 97) (dual of [219, 32, 98]-code), using
- 25 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(3¹⁸⁷, 220, F₃, 88) (dual of [220, 33, 89]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 100845 503813 820190 676322 117817 072549 703225 591007 074631 267403 014227 746484 320819 305626 578107 [i]
linear OA(3⁸, 9, F₃, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
- dual of repetition code with length 9 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(3¹⁹⁶, 229, F₃, 96) (dual of [229, 33, 97]-code)	[i]	Strength Reduction
2	Linear OA(3¹⁹⁴, 227, F₃, 95) (dual of [227, 33, 96]-code)	[i]	Truncation
3	Linear OA(3¹⁹¹, 224, F₃, 92) (dual of [224, 33, 93]-code)	[i]	Truncation
4	Linear OA(3²⁰⁷, 245, F₃, 97) (dual of [245, 38, 98]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound