MinT - Information on Result #1602062

Information on Result #1602062

Linear OOA(3⁸², 797177, F₃, 4, 9) (dual of [(797177, 4), 3188626, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁸², 797177, F₃, 2, 9) (dual of [(797177, 2), 1594272, 10]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3⁸⁰, 797176, F₃, 2, 9) (dual of [(797176, 2), 1594272, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁸⁰, 1594352, F₃, 9) (dual of [1594352, 1594272, 10]-code), using
  - constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
    1. linear OA(3⁷⁹, 1594324, F₃, 9) (dual of [1594324, 1594245, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    2. linear OA(3⁵³, 1594324, F₃, 7) (dual of [1594324, 1594271, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    3. linear OA(3²⁷, 28, F₃, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
      - dual of repetition code with length 28 [i]
    4. linear OA(3¹, 28, F₃, 1) (dual of [28, 27, 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(3⁸², 797176, F₃, 5, 9) (dual of [(797176, 5), 3985798, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁸², 797176, F₃, 12, 9) (dual of [(797176, 12), 9566030, 10]-NRT-code)	[i]		OOA Stacking with Additional Row