Several constructions of (almost) optimally extendable linear codes from MDS codes and NMDS codes.

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Bibliographic Details
Title:	Several constructions of (almost) optimally extendable linear codes from MDS codes and NMDS codes.
Authors:	LI, Wenting¹ liwenting711@163.com, HENG, Ziling^1,2 zilingheng@chd.edu.cn, LI, Xiaoru¹ lx_lixiaoru@163.com
Source:	Computer Engineering & Science / Jisuanji Gongcheng yu Kexue. Dec2025, Vol. 47 Issue 12, p2139-2149. 11p.
Subjects:	Error-correcting codes, Linear codes, Block ciphers, Parity-check matrix
Abstract:	In the implementation of block ciphers, side channel attacks(SCAs) and fault injection attacks (FIAs) are crucial cryptanalysis methods. Let 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. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

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Abstract:	In the implementation of block ciphers, side channel attacks(SCAs) and fault injection attacks (FIAs) are crucial cryptanalysis methods. Let 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. [ABSTRACT FROM AUTHOR]
ISSN:	1007130X
DOI:	10.3969/j.issn.1007-130X.2025.12.006