By Stromberg G.
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Extra info for The Asymmetry in the Distribution of Stellar Velocities
Sample text
To measure the seriousness of the error, one may define the Hamming weight |x| of a channel word x in An to be the number of nonzero letters in x. The Hamming distance between two words x, y is then |x − y|. 32) is satisfied. Indeed, |x + y| > |x| + |y| is impossible, since x + y can only have a nonzero letter in a certain slot if at least one of x and y has a nonzero letter in that slot. Moreover, |x| = 0 ⇔ x = 0. The decoding may be analyzed using the abelian group structure. 33) determines that a received word x was the result of an error xε .
And u → u1 → . . for u, then the diamond pattern occurs with w0 = uv µg . 46) takes the form uv1 µg w = uvµg uv1 µg with reduction chains v → v1 → . . and v → v1 → . . for v, the diamond pattern occurs with w0 = uv µg . 46) takes the form u1 vµg w = uvµg , uv1 µg then the diamond pattern again occurs, this time as u1 vµg w = uvµg u1 v1 µg . uv1 µg External case: Here, at least one of the initial reductions w → w1 and w → w1 is not internal. 46) takes the form t g w = u utµg µτ g u ut1 µg µτ g with a reduction t → t1 for t, then the diamond pattern occurs as t g w = u utµg µτ g t1 .
For u, then the diamond pattern occurs with w0 = uv µg . 46) takes the form uv1 µg w = uvµg uv1 µg with reduction chains v → v1 → . . and v → v1 → . . for v, the diamond pattern occurs with w0 = uv µg . 46) takes the form u1 vµg w = uvµg , uv1 µg then the diamond pattern again occurs, this time as u1 vµg w = uvµg u1 v1 µg . uv1 µg External case: Here, at least one of the initial reductions w → w1 and w → w1 is not internal. 46) takes the form t g w = u utµg µτ g u ut1 µg µτ g with a reduction t → t1 for t, then the diamond pattern occurs as t g w = u utµg µτ g t1 .