MinT - Information on Result #1299239

Information on Result #1299239

Linear OA(3²²¹, 255, F₃, 110) (dual of [255, 34, 111]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3²⁰¹, 233, F₃, 111) (dual of [233, 32, 112]-code), using
- 11 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(3²⁰¹, 235, F₃, 95) (dual of [235, 34, 96]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3²⁰¹Â > V_b^sâˆ’1(kâˆ’1)Â = 458175 385546 469580 172663 081708 552314 733921 860806 993063 144280 551921 328222 325531 336694 473504 978985 [i]
linear OA(3¹⁸, 20, F₃, 14) (dual of [20, 2, 15]-code), using
- repeating each code word 5 times [i] based on linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
  - extended Reedâ€“Solomon code RS_e(2,3) [i]
  - Hamming code H(2,3) [i]
  - Simplex code S(2,3) [i]
  - the Tetracode [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3²²¹, 255, F₃, 109) (dual of [255, 34, 110]-code)	[i]		Strength Reduction