MinT - Information on Result #1647115

Information on Result #1647115

Linear OOA(3¹⁸⁷, 523646, F₃, 5, 21) (dual of [(523646, 5), 2618043, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁷, 523646, F₃, 3, 21) (dual of [(523646, 3), 1570751, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁷, 531451, F₃, 3, 21) (dual of [(531451, 3), 1594166, 22]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹⁸⁷, 531451, F₃, 3, 22) (dual of [(531451, 3), 1594166, 23]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁸⁷, 1594353, F₃, 22) (dual of [1594353, 1594166, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
      1. linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(3¹⁵⁷, 1594323, F₃, 19) (dual of [1594323, 1594166, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(3⁴, 30, F₃, 2) (dual of [30, 26, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹⁸⁷, 261822, F₃, 25, 21) (dual of [(261822, 25), 6545363, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row