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

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Title: Several constructions of (almost) optimally extendable linear codes from MDS codes and NMDS codes.
Authors: LI, Wenting1 liwenting711@163.com, HENG, Ziling1,2 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]
Copyright of Computer Engineering & Science / Jisuanji Gongcheng yu Kexue is the property of Computer Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Several constructions of (almost) optimally extendable linear codes from MDS codes and NMDS codes.
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  Data: <searchLink fieldCode="AR" term="%22LI%2C+Wenting%22">LI, Wenting</searchLink><relatesTo>1</relatesTo><i> liwenting711@163.com</i><br /><searchLink fieldCode="AR" term="%22HENG%2C+Ziling%22">HENG, Ziling</searchLink><relatesTo>1,2</relatesTo><i> zilingheng@chd.edu.cn</i><br /><searchLink fieldCode="AR" term="%22LI%2C+Xiaoru%22">LI, Xiaoru</searchLink><relatesTo>1</relatesTo><i> lx_lixiaoru@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Computer+Engineering+%26+Science+%2F+Jisuanji+Gongcheng+yu+Kexue%22">Computer Engineering & Science / Jisuanji Gongcheng yu Kexue</searchLink>. Dec2025, Vol. 47 Issue 12, p2139-2149. 11p.
– Name: Subject
  Label: Subjects
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  Data: <searchLink fieldCode="DE" term="%22Error-correcting+codes%22">Error-correcting codes</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+codes%22">Linear codes</searchLink><br /><searchLink fieldCode="DE" term="%22Block+ciphers%22">Block ciphers</searchLink><br /><searchLink fieldCode="DE" term="%22Parity-check+matrix%22">Parity-check matrix</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computer Engineering & Science / Jisuanji Gongcheng yu Kexue is the property of Computer Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.3969/j.issn.1007-130X.2025.12.006
    Languages:
      – Code: chi
        Text: Chinese
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 2139
    Subjects:
      – SubjectFull: Error-correcting codes
        Type: general
      – SubjectFull: Linear codes
        Type: general
      – SubjectFull: Block ciphers
        Type: general
      – SubjectFull: Parity-check matrix
        Type: general
    Titles:
      – TitleFull: Several constructions of (almost) optimally extendable linear codes from MDS codes and NMDS codes.
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            NameFull: LI, Wenting
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            NameFull: HENG, Ziling
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            NameFull: LI, Xiaoru
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            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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              Value: 47
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            – TitleFull: Computer Engineering & Science / Jisuanji Gongcheng yu Kexue
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