MinT - Information on Result #1094621

Information on Result #1094621

Linear OOA(3⁵³, 531445, F₃, 5, 6) (dual of [(531445, 5), 2657172, 7]-NRT-code), using OA 3-folding and stacking based on linear OA(3⁵³, 1594335, F₃, 6) (dual of [1594335, 1594282, 7]-code), using

discarding factors / shortening the dual code based on linear OA(3⁵³, 1594337, F₃, 6) (dual of [1594337, 1594284, 7]-code), using
- 1 times truncation [i] based on linear OA(3⁵⁴, 1594338, F₃, 7) (dual of [1594338, 1594284, 8]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
    1. linear OA(3⁵³, 1594323, F₃, 7) (dual of [1594323, 1594270, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3⁴⁰, 1594323, F₃, 5) (dual of [1594323, 1594283, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(3¹⁴, 15, F₃, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
      - dual of repetition code with length 15 [i]
    4. linear OA(3¹, 15, F₃, 1) (dual of [15, 14, 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: Constructive and 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(3¹⁷⁴, 2209165, F₃, 5, 13) (dual of [(2209165, 5), 11045651, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3⁵³, 531445, F₃, 6, 6) (dual of [(531445, 6), 3188617, 7]-NRT-code)	[i]		Appending kth Column