MinT - Information on Result #1437889

Information on Result #1437889

Linear OOA(5⁹⁵, 13134, F₅, 2, 19) (dual of [(13134, 2), 26173, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5⁹⁵, 13134, F₅, 19) (dual of [13134, 13039, 20]-code), using

discarding factors / shortening the dual code based on linear OA(5⁹⁵, 15647, F₅, 19) (dual of [15647, 15552, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5⁹⁴, 15646, F₅, 19) (dual of [15646, 15552, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
    1. linear OA(5⁹¹, 15625, F₅, 19) (dual of [15625, 15534, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(5⁷³, 15625, F₅, 16) (dual of [15625, 15552, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(5³, 21, F₅, 2) (dual of [21, 18, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(5³, 24, F₅, 2) (dual of [24, 21, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 24Â = 5²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(5⁹⁵, 6567, F₅, 3, 19) (dual of [(6567, 3), 19606, 20]-NRT-code)	[i]		OOA Folding