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Coding Theory : Linear Code, Coset Leaders and Vector Weight

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Let x+C be a coset, and assume x+c, x+e have weight less or equal than t....
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Coset leaders and vector weight are investigated. The weight of the functions are determined.

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Let x+C be a coset, and assume x+c, x+e have weight less or equal than t. Then:

for every a. This implies: (take a=-x).

The hypothesis implies:

.

2t=d-1 or 2t=d, depending on the parity of d.

If c and e are distinct, ...

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