MinT - Information on Result #1299258

Information on Result #1299258

Linear OA(3²²², 256, F₃, 111) (dual of [256, 34, 112]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3²⁰², 234, F₃, 112) (dual of [234, 32, 113]-code), using
- 10 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(3²⁰², 236, F₃, 96) (dual of [236, 34, 97]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3²⁰²Â > V_b^sâˆ’1(kâˆ’1)Â = 2 278638 945808 087567 485892 085145 468379 065686 417460 023423 009772 850310 815008 291503 689523 347072 346235 [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(3²²⁰, 254, F₃, 109) (dual of [254, 34, 110]-code)	[i]		Truncation