MinT - Information on Result #1298832

Information on Result #1298832

Linear OA(3¹⁷⁹, 201, F₃, 92) (dual of [201, 22, 93]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁶⁴, 184, F₃, 92) (dual of [184, 20, 93]-code), using
- constructionÂ X applied to C_e(91) âŠ‚ C_e(90) [i] based on
  1. linear OA(3¹⁶⁴, 183, F₃, 92) (dual of [183, 19, 93]-code), using an extension C_e(91) of the narrow-sense BCH-code C(I) with length 182Â | 3⁶âˆ’1, defining interval IÂ =Â [1,91], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 92 [i]
  2. linear OA(3¹⁶³, 183, F₃, 91) (dual of [183, 20, 92]-code), using an extension C_e(90) of the narrow-sense BCH-code C(I) with length 182Â | 3⁶âˆ’1, defining interval IÂ =Â [1,90], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 91 [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(3¹⁶⁴, 186, F₃, 81) (dual of [186, 22, 82]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 1 026419 836656 840939 491717 121974 784551 268829 673264 547112 164338 859154 887792 895011 [i]
linear OA(3¹³, 15, F₃, 10) (dual of [15, 2, 11]-code), using
- 1 times truncation [i] based on linear OA(3¹⁴, 16, F₃, 11) (dual of [16, 2, 12]-code), using
  - repeating each code word 4 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.