Abstract
We prove that every [n, k, d] q code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and \({d \equiv -1 \pmod{q}}\) is extendable unless its diversity is \({\left({q \choose 2}q^{k-3}+\theta_{k-3}, {q\choose 2}q^{k-3}\right)}\) for odd q, where \({\theta_j = (q^{j+1}-1)/(q-1)}\) .
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Communicated by R. Hill.
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Cheon, E.J., Maruta, T. A new extension theorem for 3-weight modulo q linear codes over \({\mathbb{F}_q}\) . Des. Codes Cryptogr. 52, 171–183 (2009). https://doi.org/10.1007/s10623-009-9275-1
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DOI: https://doi.org/10.1007/s10623-009-9275-1