MinT - Information on Result #1520547

Information on Result #1520547

Linear OOA(3⁵¹, 531469, F₃, 3, 6) (dual of [(531469, 3), 1594356, 7]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3⁵¹, 531469, F₃, 6) (dual of [531469, 531418, 7]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(3⁵⁰, 531467, F₃, 6) (dual of [531467, 531417, 7]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(3) [i] based on
    1. linear OA(3⁴⁹, 531441, F₃, 7) (dual of [531441, 531392, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3²⁵, 531441, F₃, 4) (dual of [531441, 531416, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(3²⁵, 26, F₃, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
      - dual of repetition code with length 26 [i]
    4. linear OA(3¹, 26, F₃, 1) (dual of [26, 25, 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(3⁵⁰, 531468, F₃, 5) (dual of [531468, 531418, 6]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 53187 635733 407401 626299 [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]

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(3⁵¹, 531468, F₃, 4, 6) (dual of [(531468, 4), 2125821, 7]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁵¹, 531468, F₃, 5, 6) (dual of [(531468, 5), 2657289, 7]-NRT-code)	[i]		OOA Stacking with Additional Row