MDS codes over finite principal ideal rings
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Publication:1009097
DOI10.1007/s10623-008-9215-5zbMath1178.94221OpenAlexW2011810490MaRDI QIDQ1009097
Jon-Lark Kim, Steven T. Dougherty, Hamid Kulosman
Publication date: 31 March 2009
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10623-008-9215-5
Related Items (27)
ON SOME CLASSES OF FUNCTIONS AND HYPERCUBES ⋮ Two self-dual codes with larger lengths over ℤ9 ⋮ Codes over \(\mathfrak{m}\)-adic completion rings ⋮ On counting subring-submodules of free modules over finite commutative Frobenius rings ⋮ Quadratic residue codes over \(\mathbb{F}_{p^r}+{u_1}\mathbb{F}_{p^r}+{u_2}\mathbb{F}_{p^r}+\dots+{u_t}\mathbb{F}_ {p^r}\) ⋮ Self-dual codes over commutative Frobenius rings ⋮ Matrix graphs and MRD codes over finite principal ideal rings ⋮ Higher weights for codes over rings ⋮ LCP of group codes over finite Frobenius rings ⋮ Construction of self-dual MDR cyclic codes over finite chain rings ⋮ Negacyclic self-dual codes over finite chain rings ⋮ Additive codes over Galois rings ⋮ Linear complementary pairs of codes over rings ⋮ Non-invertible-element constacyclic codes over finite PIRs ⋮ \(\mathbb{F}_q\)-linear codes over \(\mathbb{F}_q\)-algebras ⋮ DNA cyclic codes over rings ⋮ Codes over an infinite family of rings with a Gray map ⋮ MDS and self-dual codes over rings ⋮ Constacyclic Codes over Finite Principal Ideal Rings ⋮ Skew-cyclic codes over \(B_k\) ⋮ Structure of linear codes over the ring \(B_k\) ⋮ Counting codes over rings ⋮ Independence of vectors in codes over rings ⋮ Construction of MDS self-dual codes over Galois rings ⋮ The 2-distance coloring of the Cartesian product of cycles using optimal Lee codes ⋮ Linear complementary dual codes over rings ⋮ Quantum codes over rings
Cites Work
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- Finite-ring combinatorics and MacWilliams' equivalence theorem
- Linear codes over finite chain rings
- Self-dual codes and invariant theory
- Lifted codes and their weight enumerators
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- On BCH codes over arbitrary integer tings (Corresp.)
- Codes over integer residue rings
- Codes over Zm
- Codes over Zm, revisited
- Duality for modules over finite rings and applications to coding theory
- The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
- MDR codes over Z/sub k/
- On the Hamming distance of linear codes over a finite chain ring
- OPTIMAL LINEAR CODES OVER ℤm
- Codes over certain rings
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