MinT - Information on Result #1525204

Information on Result #1525204

Linear OOA(3¹⁶⁴, 74318, F₃, 3, 21) (dual of [(74318, 3), 222790, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁴, 74318, F₃, 2, 21) (dual of [(74318, 2), 148472, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁴, 88600, F₃, 2, 21) (dual of [(88600, 2), 177036, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁴, 177200, F₃, 21) (dual of [177200, 177036, 22]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [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(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁹, 53, F₃, 4) (dual of [53, 44, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁶⁴, 37159, F₃, 5, 21) (dual of [(37159, 5), 185631, 22]-NRT-code)	[i]		OOA Folding