FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3202718886> ?p ?o ?g. }

• W3202718886 endingPage "7984" @default.
• W3202718886 startingPage "7964" @default.
• W3202718886 abstract "Let <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$q=p^{e}$ </tex-math></inline-formula> be a prime power and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> be an integer with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$0leq ell leq e-1$ </tex-math></inline-formula> . The <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> -Galois hull of classical linear codes is a generalization of the Euclidean hull and Hermitian hull. We provide a necessary and sufficient condition under which a codeword of a GRS code or an extended GRS code belongs to its <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> -Galois dual code, generalizing both the Euclidean case and Hermitian case in the literature. By using four different tools: 1) the norm mapping from <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {F}_{q}^{ast }$ </tex-math></inline-formula> to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {F}_{p^{ell }}^{ast }$ </tex-math></inline-formula> ; 2) the direct product of two cyclic subgroups; 3) the coset decomposition of a cyclic group; 4) an additive subgroup of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathbb {F}_{q}$ </tex-math></inline-formula> and its cosets, we construct eleven families of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$q$ </tex-math></inline-formula> -ary MDS codes with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> -Galois hulls of arbitrary dimensions, and give the related eleven families of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$[[n,k,d;c]]_{q}$ </tex-math></inline-formula> entanglement-assisted quantum error-correcting codes (EAQECCs) with relatively large minimum distance in the sense that <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$2d=n-k+2+c$ </tex-math></inline-formula> . We show that developing the theory on <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> -Galois hulls of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$q$ </tex-math></inline-formula> -ary MDS codes in this paper enables us to obtain new <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$q$ </tex-math></inline-formula> -ary EAQECCs with different kinds of length sets via different <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ell $ </tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$2ell mid e$ </tex-math></inline-formula> ." @default.
• W3202718886 created "2021-10-11" @default.
• W3202718886 creator A5067002890 @default.
• W3202718886 date "2021-12-01" @default.
• W3202718886 modified "2023-10-14" @default.
• W3202718886 title "MDS Codes With Galois Hulls of Arbitrary Dimensions and the Related Entanglement-Assisted Quantum Error Correction" @default.
• W3202718886 cites W1613141042 @default.
• W3202718886 cites W1903020140 @default.
• W3202718886 cites W1965035185 @default.
• W3202718886 cites W1967817162 @default.
• W3202718886 cites W1977835025 @default.
• W3202718886 cites W1978924226 @default.
• W3202718886 cites W1982432882 @default.
• W3202718886 cites W1999706070 @default.
• W3202718886 cites W2002370994 @default.
• W3202718886 cites W2020636832 @default.
• W3202718886 cites W2040653896 @default.
• W3202718886 cites W2051471360 @default.
• W3202718886 cites W2060784542 @default.
• W3202718886 cites W2063592138 @default.
• W3202718886 cites W2067100062 @default.
• W3202718886 cites W2069711632 @default.
• W3202718886 cites W2076107177 @default.
• W3202718886 cites W2082000686 @default.
• W3202718886 cites W2084891113 @default.
• W3202718886 cites W2091331782 @default.
• W3202718886 cites W2095025840 @default.
• W3202718886 cites W2095090362 @default.
• W3202718886 cites W2114207424 @default.
• W3202718886 cites W2138142977 @default.
• W3202718886 cites W2143438504 @default.
• W3202718886 cites W2165026273 @default.
• W3202718886 cites W2167413626 @default.
• W3202718886 cites W2593067933 @default.
• W3202718886 cites W2755639496 @default.
• W3202718886 cites W2763302490 @default.
• W3202718886 cites W2785335201 @default.
• W3202718886 cites W2884492656 @default.
• W3202718886 cites W2895580676 @default.
• W3202718886 cites W2897844431 @default.
• W3202718886 cites W2962682082 @default.
• W3202718886 cites W2963105100 @default.
• W3202718886 cites W2963616848 @default.
• W3202718886 cites W2963637464 @default.
• W3202718886 cites W2963734035 @default.
• W3202718886 cites W2963803325 @default.
• W3202718886 cites W2963998610 @default.
• W3202718886 cites W2989678375 @default.
• W3202718886 cites W2989802578 @default.
• W3202718886 cites W3003401666 @default.
• W3202718886 cites W3040174801 @default.
• W3202718886 cites W3098032907 @default.
• W3202718886 cites W3098999158 @default.
• W3202718886 cites W3099628384 @default.
• W3202718886 cites W3100206575 @default.
• W3202718886 cites W3100713059 @default.
• W3202718886 cites W3101905439 @default.
• W3202718886 cites W3102121229 @default.
• W3202718886 cites W3106210707 @default.
• W3202718886 cites W3144380511 @default.
• W3202718886 cites W3157471403 @default.
• W3202718886 doi "https://doi.org/10.1109/tit.2021.3117562" @default.
• W3202718886 hasPublicationYear "2021" @default.
• W3202718886 type Work @default.
• W3202718886 sameAs 3202718886 @default.
• W3202718886 citedByCount "13" @default.
• W3202718886 countsByYear W32027188862022 @default.
• W3202718886 countsByYear W32027188862023 @default.
• W3202718886 crossrefType "journal-article" @default.
• W3202718886 hasAuthorship W3202718886A5067002890 @default.
• W3202718886 hasConcept C114614502 @default.
• W3202718886 hasConcept C118615104 @default.
• W3202718886 hasConcept C127413603 @default.
• W3202718886 hasConcept C136119220 @default.
• W3202718886 hasConcept C199104240 @default.
• W3202718886 hasConcept C202444582 @default.
• W3202718886 hasConcept C33923547 @default.
• W3202718886 hasConcept C37423430 @default.
• W3202718886 hasConcept C45357846 @default.
• W3202718886 hasConcept C94375191 @default.
• W3202718886 hasConceptScore W3202718886C114614502 @default.
• W3202718886 hasConceptScore W3202718886C118615104 @default.
• W3202718886 hasConceptScore W3202718886C127413603 @default.
• W3202718886 hasConceptScore W3202718886C136119220 @default.
• W3202718886 hasConceptScore W3202718886C199104240 @default.
• W3202718886 hasConceptScore W3202718886C202444582 @default.
• W3202718886 hasConceptScore W3202718886C33923547 @default.
• W3202718886 hasConceptScore W3202718886C37423430 @default.
• W3202718886 hasConceptScore W3202718886C45357846 @default.
• W3202718886 hasConceptScore W3202718886C94375191 @default.
• W3202718886 hasIssue "12" @default.
• W3202718886 hasLocation W32027188861 @default.
• W3202718886 hasOpenAccess W3202718886 @default.
• W3202718886 hasPrimaryLocation W32027188861 @default.
• W3202718886 hasRelatedWork W161301265 @default.
• W3202718886 hasRelatedWork W1998317259 @default.
• W3202718886 hasRelatedWork W2007256320 @default.
• W3202718886 hasRelatedWork W2377576908 @default.

• next