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fix docstring whitespaces
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Ivo-Maffei committed Jul 13, 2020
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13 changes: 7 additions & 6 deletions src/sage/coding/kasami_codes.pyx
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Expand Up @@ -9,23 +9,24 @@ The extended Kasami code with parameters `(s,t)` is defined as
.. MATH::
\{ v \in GF(2)^s \mid
\sum_{a \in GF(s)} v_a =
\sum_{a \in GF(s)} a v_a =
\sum_{a \in GF(s)} a^{t+1} v_a = 0 \}
\{ v \in GF(2)^s \mid
\sum_{a \in GF(s)} v_a =
\sum_{a \in GF(s)} a v_a =
\sum_{a \in GF(s)} a^{t+1} v_a = 0 \}
It follows that these are subfield subcodes of
the code having those three equations as parity checks.
The only valid parameters `s,t` are given by the below,
where `q` is a power of 2:
where `q` is a power of 2:
* `s = q^{2j+1}`, `t = q^m` with `m \leq j` and `\gcd(m,2j+1) = 1`
* `s = q^2`, `t=q`
The coset graphs of the Kasami codes are distance-regular.
In particular, the extended Kasami codes result in
distance-regular graphs with intersection arrays:
distance-regular graphs with intersection arrays:
* `[q^{2j+1}, q^{2j+1} - 1, q^{2j+1} - q, q^{2j+1} - q^{2j} + 1;`
`1, q, q^{2j} -1, q^{2j+1}]`
* `[q^2, q^2 - 1, q^2 - q, 1; 1, q, q^2 - 1, q^2]`
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