Abstract
Due to their wide applications in communications, data storage and cryptography, linear codes have received much attention in the past decades. The objective of this paper is to construct a family of linear codes over ${\mathbb F}_{q}$, where q is a prime power. This family of codes has length (qk − 1)t, dimension ek, where k ≥ 2 and e, t are arbitrary integers with 2 ≤ e ≤ t . In some cases, this class of linear codes is distance-optimal with respect to the Griesmer bound. The weight distribution of this family of linear codes is also determined. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.
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