MinT - Information on Result #1605588

Information on Result #1605588

Linear OOA(3¹⁵⁸, 48472, F₃, 4, 22) (dual of [(48472, 4), 193730, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁸, 48472, F₃, 3, 22) (dual of [(48472, 3), 145258, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁸, 59053, F₃, 3, 22) (dual of [(59053, 3), 177001, 23]-NRT-code), using
- 3² times duplication [i] based on linear OOA(3¹⁵⁶, 59053, F₃, 3, 22) (dual of [(59053, 3), 177003, 23]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁵⁶, 177159, F₃, 22) (dual of [177159, 177003, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [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(3¹⁴⁴, 177147, F₃, 20) (dual of [177147, 177003, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹⁵⁸, 16157, F₃, 28, 22) (dual of [(16157, 28), 452238, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row