MinT - Information on Result #1299144

Information on Result #1299144

Linear OA(3²⁰⁸, 241, F₃, 105) (dual of [241, 33, 106]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁹⁵, 227, F₃, 105) (dual of [227, 32, 106]-code), using
- 17 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(3¹⁹⁵, 228, F₃, 92) (dual of [228, 33, 93]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁹⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 482 042856 633233 415572 291241 156385 048140 901997 148040 114756 348677 887213 312131 169180 377376 875675 [i]
linear OA(3¹², 13, F₃, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
- dual of repetition code with length 13 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3²⁰⁸, 241, F₃, 104) (dual of [241, 33, 105]-code)	[i]		Strength Reduction
2	Linear OA(3²⁰⁸, 241, F₃, 103) (dual of [241, 33, 104]-code)	[i]		Strength Reduction