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Linear codes with few weights have many applications in secret sharingschemes, authentication codes, communication and strongly regular graphs. Inthis paper, we consider linear codes with three weights in arbitrarycharacteristic. To do this, we generalize the recent contribution of Mesnagergiven in [Cryptography and Communications 9(1), 71-84, 2017]. We first presenta new class of binary linear codes with three weights from plateaued Booleanfunctions and their weight distributions. We next introduce the notion of(weakly) regular plateaued functions in odd characteristic $p$ and giveconcrete examples of these functions. Moreover, we construct a new class ofthree-weight linear $p$-ary codes from weakly regular plateaued functions anddetermine their weight distributions. We finally analyse the constructed linearcodes for secret sharing schemes.

A new class of three-weight linear codes from weakly regular plateaued functions