MinT - Information on Result #1549211

Information on Result #1549211

Linear OOA(5¹¹¹, 59779, F₅, 3, 19) (dual of [(59779, 3), 179226, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹¹¹, 59779, F₅, 19) (dual of [59779, 59668, 20]-code), using

discarding factors / shortening the dual code based on linear OA(5¹¹¹, 78152, F₅, 19) (dual of [78152, 78041, 20]-code), using
- constructionÂ XX applied to C_e(18) âŠ‚ C_e(15) âŠ‚ C_e(13) [i] based on
  1. linear OA(5¹⁰⁶, 78125, F₅, 19) (dual of [78125, 78019, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(5⁸⁵, 78125, F₅, 16) (dual of [78125, 78040, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(5⁷⁸, 78125, F₅, 14) (dual of [78125, 78047, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  4. linear OA(5³, 25, F₅, 2) (dual of [25, 22, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
      - Hamming code H(3,5) [i]
  5. linear OA(5¹, 2, F₅, 1) (dual of [2, 1, 2]-code), using
    - dual of repetition code with length 2 [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(5¹¹¹, 19926, F₅, 21, 19) (dual of [(19926, 21), 418335, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row