MinT - Information on Result #1647501

Information on Result #1647501

Linear OOA(3¹⁹², 531461, F₃, 5, 21) (dual of [(531461, 5), 2657113, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹², 531461, F₃, 3, 21) (dual of [(531461, 3), 1594191, 22]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁹², 1594383, F₃, 21) (dual of [1594383, 1594191, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁹², 1594384, F₃, 21) (dual of [1594384, 1594192, 22]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁹, 61, F₃, 4) (dual of [61, 52, 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(3¹⁹³, 531461, F₃, 5, 21) (dual of [(531461, 5), 2657112, 22]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁹², 265730, F₃, 25, 21) (dual of [(265730, 25), 6643058, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row