MinT - Information on Result #1606937

Information on Result #1606937

Linear OOA(3¹⁷⁸, 164336, F₃, 4, 22) (dual of [(164336, 4), 657166, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁸, 164336, F₃, 3, 22) (dual of [(164336, 3), 492830, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁸, 177162, F₃, 3, 22) (dual of [(177162, 3), 531308, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁷⁸, 531486, F₃, 22) (dual of [531486, 531308, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
    1. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(3¹³³, 531441, F₃, 17) (dual of [531441, 531308, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 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(3¹⁷⁸, 54778, F₃, 28, 22) (dual of [(54778, 28), 1533606, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row