MinT - Information on Result #1532090

Information on Result #1532090

Linear OOA(3²³⁷, 25667, F₃, 3, 34) (dual of [(25667, 3), 76764, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁷, 25667, F₃, 2, 34) (dual of [(25667, 2), 51097, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁷, 29557, F₃, 2, 34) (dual of [(29557, 2), 58877, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²³⁷, 59114, F₃, 34) (dual of [59114, 58877, 35]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²³⁷, 59115, F₃, 34) (dual of [59115, 58878, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(25) [i] based on
      1. linear OA(3²²¹, 59049, F₃, 34) (dual of [59049, 58828, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. linear OA(3¹⁷¹, 59049, F₃, 26) (dual of [59049, 58878, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(3¹⁶, 66, F₃, 7) (dual of [66, 50, 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(3²³⁷, 12833, F₃, 5, 34) (dual of [(12833, 5), 63928, 35]-NRT-code)	[i]		OOA Folding