MinT - Information on Result #1601809

Information on Result #1601809

Linear OOA(3⁷³, 2391493, F₃, 4, 8) (dual of [(2391493, 4), 9565899, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷³, 2391493, F₃, 2, 8) (dual of [(2391493, 2), 4782913, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁷³, 4782986, F₃, 8) (dual of [4782986, 4782913, 9]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3⁷², 4782985, F₃, 8) (dual of [4782985, 4782913, 9]-code), using
  - constructionÂ X4 applied to C_e(7) âŠ‚ C_e(6) [i] based on
    1. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(3¹⁵, 16, F₃, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
      - dual of repetition code with length 16 [i]
    4. linear OA(3¹, 16, F₃, 1) (dual of [16, 15, 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, k and s, k and t, m and s, m 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(3⁷³, 2391492, F₃, 5, 8) (dual of [(2391492, 5), 11957387, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁷³, 2391492, F₃, 12, 8) (dual of [(2391492, 12), 28697831, 9]-NRT-code)	[i]		OOA Stacking with Additional Row