MinT - Information on Result #1601703

Information on Result #1601703

Linear OOA(3⁶⁹, 797170, F₃, 4, 8) (dual of [(797170, 4), 3188611, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁶⁹, 797170, F₃, 2, 8) (dual of [(797170, 2), 1594271, 9]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3⁶⁷, 797169, F₃, 2, 8) (dual of [(797169, 2), 1594271, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁶⁷, 1594338, F₃, 8) (dual of [1594338, 1594271, 9]-code), using
  - constructionÂ X4 applied to C_e(7) âŠ‚ C_e(6) [i] based on
    1. linear OA(3⁶⁶, 1594323, F₃, 8) (dual of [1594323, 1594257, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. 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]
    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: 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(3⁶⁹, 797169, F₃, 5, 8) (dual of [(797169, 5), 3985776, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁶⁹, 797169, F₃, 12, 8) (dual of [(797169, 12), 9565959, 9]-NRT-code)	[i]		OOA Stacking with Additional Row