MinT - Information on Result #1520417

Information on Result #1520417

Linear OOA(3⁴³, 29531, F₃, 3, 7) (dual of [(29531, 3), 88550, 8]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁴³, 29531, F₃, 2, 7) (dual of [(29531, 2), 59019, 8]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁴³, 59062, F₃, 7) (dual of [59062, 59019, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3⁴², 59061, F₃, 7) (dual of [59061, 59019, 8]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
    1. linear OA(3⁴¹, 59049, F₃, 7) (dual of [59049, 59008, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3³¹, 59049, F₃, 5) (dual of [59049, 59018, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(3¹¹, 12, F₃, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
      - dual of repetition code with length 12 [i]
    4. 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]

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(3⁴³, 29530, F₃, 4, 7) (dual of [(29530, 4), 118077, 8]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁴³, 29530, F₃, 5, 7) (dual of [(29530, 5), 147607, 8]-NRT-code)	[i]
3	Linear OOA(3⁴³, 29530, F₃, 9, 7) (dual of [(29530, 9), 265727, 8]-NRT-code)	[i]