MinT - Information on Result #1301778

Information on Result #1301778

Linear OA(5¹²¹, 78163, F₅, 20) (dual of [78163, 78042, 21]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹¹⁸, 78158, F₅, 20) (dual of [78158, 78040, 21]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(15) [i] based on
  1. linear OA(5¹¹³, 78125, F₅, 21) (dual of [78125, 78012, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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(5⁵, 33, F₅, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using
    - discarding factors / shortening the dual code based on linear OA(5⁵, 42, F₅, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
      - large caps in PG(4,Â b) [i]
linear OA(5¹¹⁸, 78160, F₅, 18) (dual of [78160, 78042, 19]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹¹⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 7 309069 901290 073384 883047 833310 024926 645612 110152 243656 144992 535681 611005 159565 [i]
linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(5¹²¹, 78163, F₅, 2, 20) (dual of [(78163, 2), 156205, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(5¹²¹, 78163, F₅, 3, 20) (dual of [(78163, 3), 234368, 21]-NRT-code)	[i]
3	Digital (101, 121, 78163)-net over F₅	[i]