MinT - Information on Result #2507142

Information on Result #2507142

Linear OOA(7⁹⁸, 57, F₇, 2, 65) (dual of [(57, 2), 16, 66]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(7⁹⁶, 56, F₇, 2, 65) (dual of [(56, 2), 16, 66]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁹, 8, F₇, 2, 9) (dual of [(8, 2), 7, 10]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;7,7) [i]
2. linear OOA(7¹⁰, 8, F₇, 2, 10) (dual of [(8, 2), 6, 11]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;6,7) [i]
3. linear OOA(7¹³, 8, F₇, 2, 13) (dual of [(8, 2), 3, 14]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;3,7) [i]
4. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
6. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
7. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)

Mode: Constructive and 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(7⁹⁹, 57, F₇, 2, 65) (dual of [(57, 2), 15, 66]-NRT-code)	[i]		OOA Duplication