MinT - Information on Result #1411385

Information on Result #1411385

Linear OOA(3¹⁵¹, 740, F₃, 2, 37) (dual of [(740, 2), 1329, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁵¹, 740, F₃, 37) (dual of [740, 589, 38]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁵¹, 763, F₃, 37) (dual of [763, 612, 38]-code), using
- constructionÂ XX applied to C₁Â =Â C([722,28]), C₂Â =Â C([0,30]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,28]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([722,30]) [i] based on
  1. linear OA(3¹³⁶, 728, F₃, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
  2. linear OA(3¹¹⁸, 728, F₃, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
  3. linear OA(3¹⁴², 728, F₃, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,30}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  4. linear OA(3¹¹², 728, F₃, 29) (dual of [728, 616, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
  5. linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
  6. linear OA(3¹, 7, F₃, 1) (dual of [7, 6, 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(3¹⁵¹, 370, F₃, 3, 37) (dual of [(370, 3), 959, 38]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁵¹, 370, F₃, 4, 37) (dual of [(370, 4), 1329, 38]-NRT-code)	[i]		OOA Folding