MinT - Information on Result #1604347

Information on Result #1604347

Linear OOA(3¹³⁶, 562570, F₃, 4, 15) (dual of [(562570, 4), 2250144, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁶, 562570, F₃, 2, 15) (dual of [(562570, 2), 1125004, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁶, 797178, F₃, 2, 15) (dual of [(797178, 2), 1594220, 16]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3¹³², 797176, F₃, 2, 15) (dual of [(797176, 2), 1594220, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹³², 1594352, F₃, 15) (dual of [1594352, 1594220, 16]-code), using
    - constructionÂ X4 applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(3¹³¹, 1594324, F₃, 15) (dual of [1594324, 1594193, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(3¹⁰⁵, 1594324, F₃, 13) (dual of [1594324, 1594219, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(3¹³⁶, 281284, F₃, 20, 15) (dual of [(281284, 20), 5625544, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row