MinT - Information on Result #1644469

Information on Result #1644469

Linear OOA(3¹⁴⁷, 177156, F₃, 5, 18) (dual of [(177156, 5), 885633, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁷, 177156, F₃, 3, 18) (dual of [(177156, 3), 531321, 19]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁴⁷, 531468, F₃, 18) (dual of [531468, 531321, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁴⁶, 531467, F₃, 18) (dual of [531467, 531321, 19]-code), using
  - constructionÂ X4 applied to C_e(18) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹⁴⁵, 531441, F₃, 19) (dual of [531441, 531296, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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]

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(3¹⁴⁸, 177156, F₃, 5, 18) (dual of [(177156, 5), 885632, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁴⁹, 177156, F₃, 5, 18) (dual of [(177156, 5), 885631, 19]-NRT-code)	[i]		OOA Duplication