Abstract: In the implementation of block ciphers, side channel attacks(SCAs) and fault injection attacks(FIAs) are crucial cryptanalysis methods. Let C  be a linear code over Fq  with a generator matrix G, and C′  be a linear code over Fq  with a generator matrix G′=［G:Ik］, where Ik   is the identity matrix of order  k. If  d(C′⊥)=d(C⊥), then C  is said to be an optimally extendable linear code; if  d(C′⊥)= d(C⊥)－1, then C  is said to be an almost optimally extendable linear code. Optimally or almost optimally extendable linear codes effectively protect not only sensitive data stored in registers from SCAs and FIAs but also the entire algorithm. A class of almost optimally extendable linear codes with dimension 5 is constructed by special generator matrices, and its parameters and weight enumerators are obtained. In addition, it is proved that another 4 classes of NMDS (near maximum distance separable) codes with dimension 5 and 2 classes of NMDS codes with dimension 4 are optimally extendable linear codes. In particular, the parameters of the (almost) optimally extendable linear codes are different from those of known (almost) optimally extendable linear codes, and the  constructed codes have potential applications in direct sum masking.

Key words: linear code, extendable code, weight enumerator