MinT - Information on Result #1533620

Information on Result #1533620

Linear OOA(3²⁴⁹, 2219, F₃, 3, 52) (dual of [(2219, 3), 6408, 53]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁴⁹, 2219, F₃, 52) (dual of [2219, 1970, 53]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁴⁹, 2223, F₃, 52) (dual of [2223, 1974, 53]-code), using
- constructionÂ X applied to C_e(51) âŠ‚ C_e(45) [i] based on
  1. linear OA(3²³⁹, 2187, F₃, 52) (dual of [2187, 1948, 53]-code), using an extension C_e(51) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,51], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [i]
  2. linear OA(3²¹¹, 2187, F₃, 46) (dual of [2187, 1976, 47]-code), using an extension C_e(45) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,45], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 46 [i]
  3. linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      3. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(3) [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 OOA(3²⁴⁹, 1109, F₃, 5, 52) (dual of [(1109, 5), 5296, 53]-NRT-code)	[i]		OOA Folding