MinT - Information on Result #1651593

Information on Result #1651593

Linear OOA(3²³⁹, 61699, F₃, 5, 31) (dual of [(61699, 5), 308256, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁹, 61699, F₃, 2, 31) (dual of [(61699, 2), 123159, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁹, 88610, F₃, 2, 31) (dual of [(88610, 2), 176981, 32]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²³⁷, 88609, F₃, 2, 31) (dual of [(88609, 2), 176981, 32]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²³⁷, 177218, F₃, 31) (dual of [177218, 176981, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(22) [i] based on
      1. linear OA(3²²¹, 177147, F₃, 31) (dual of [177147, 176926, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(3¹⁶⁶, 177147, F₃, 23) (dual of [177147, 176981, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3¹⁶, 71, F₃, 7) (dual of [71, 55, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3²³⁹, 20566, F₃, 35, 31) (dual of [(20566, 35), 719571, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row