MinT - Information on Result #1645443

Information on Result #1645443

Linear OOA(3¹⁶³, 69916, F₃, 5, 21) (dual of [(69916, 5), 349417, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶³, 69916, F₃, 2, 21) (dual of [(69916, 2), 139669, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶³, 88594, F₃, 2, 21) (dual of [(88594, 2), 177025, 22]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹⁶³, 88594, F₃, 2, 22) (dual of [(88594, 2), 177025, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶³, 177188, F₃, 22) (dual of [177188, 177025, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
      1. linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(3¹²², 177147, F₃, 17) (dual of [177147, 177025, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹⁶³, 34957, F₃, 25, 21) (dual of [(34957, 25), 873762, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row