MinT - Information on Result #1437855

Information on Result #1437855

Linear OOA(5⁹⁴, 345389, F₅, 2, 14) (dual of [(345389, 2), 690684, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5⁹⁴, 345389, F₅, 14) (dual of [345389, 345295, 15]-code), using

discarding factors / shortening the dual code based on linear OA(5⁹⁴, 390655, F₅, 14) (dual of [390655, 390561, 15]-code), using
- constructionÂ XX applied to C_e(13) âŠ‚ C_e(10) âŠ‚ C_e(8) [i] based on
  1. linear OA(5⁸⁹, 390625, F₅, 14) (dual of [390625, 390536, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  2. linear OA(5⁶⁵, 390625, F₅, 11) (dual of [390625, 390560, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(5⁵⁷, 390625, F₅, 9) (dual of [390625, 390568, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  4. linear OA(5³, 28, F₅, 2) (dual of [28, 25, 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(5⁹⁴, 172694, F₅, 3, 14) (dual of [(172694, 3), 517988, 15]-NRT-code)	[i]		OOA Folding