MinT - Information on Result #2449489

Information on Result #2449489

Linear OOA(7¹¹⁰, 57, F₇, 2, 94) (dual of [(57, 2), 4, 95]-NRT-code), using strength reduction based on linear OOA(7¹¹⁰, 57, F₇, 2, 96) (dual of [(57, 2), 4, 97]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(7¹², 8, F₇, 2, 12) (dual of [(8, 2), 4, 13]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;4,7) [i]
2. linear OOA(7⁹⁴, 49, F₇, 2, 83) (dual of [(49, 2), 4, 84]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(7¹¹, 7, F₇, 2, 11) (dual of [(7, 2), 3, 12]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;3,7) [i]
    2. linear OOA(7¹³, 7, F₇, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
      - dual of repetition NRT-code with length 7 [i]
      - Reedâ€“Solomon NRT-code RS(2;1,7) [i]
    3. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
    5. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
    6. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
    7. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-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(7⁹⁸, 51, F₇, 2, 82) (dual of [(51, 2), 4, 83]-NRT-code)	[i]		Truncation for OOAs