MinT - Information on Result #1522445

Information on Result #1522445

Linear OOA(3¹¹⁴, 75058, F₃, 3, 15) (dual of [(75058, 3), 225060, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹⁴, 75058, F₃, 2, 15) (dual of [(75058, 2), 150002, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹¹⁴, 88587, F₃, 2, 15) (dual of [(88587, 2), 177060, 16]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹¹², 88586, F₃, 2, 15) (dual of [(88586, 2), 177060, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹¹², 177172, F₃, 15) (dual of [177172, 177060, 16]-code), using
    - constructionÂ X4 applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(3¹¹¹, 177148, F₃, 15) (dual of [177148, 177037, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(3⁸⁹, 177148, F₃, 13) (dual of [177148, 177059, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(3²³, 24, F₃, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
        dual of repetition code with length 24 [i]
      4. linear OA(3¹, 24, F₃, 1) (dual of [24, 23, 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(3¹¹⁴, 37529, F₃, 5, 15) (dual of [(37529, 5), 187531, 16]-NRT-code)	[i]		OOA Folding