MinT - Information on Result #1647970

Information on Result #1647970

Linear OOA(3¹⁹⁸, 27980, F₃, 5, 28) (dual of [(27980, 5), 139702, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁸, 27980, F₃, 2, 28) (dual of [(27980, 2), 55762, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹⁸, 29558, F₃, 2, 28) (dual of [(29558, 2), 58918, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁹⁸, 59116, F₃, 28) (dual of [59116, 58918, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(19) [i] based on
    1. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(3¹⁷, 67, F₃, 7) (dual of [67, 50, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁷, 80, F₃, 7) (dual of [80, 63, 8]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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(3¹⁹⁸, 9326, F₃, 35, 28) (dual of [(9326, 35), 326212, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row