Results 61 to 70 of about 290,159 (337)
Hermitian Rank Metric Codes and Duality
IEEE Access, 2021 In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for $\mathbb {F}_{q^{2}}$ -linear matrix codes in the ambient space $(\mathbb {F}_{q^{2}})_{n,m}$ and for both $\mathbb {F}_{q^{2}}$ -additive ...
Javier De La Cruz +2 more
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Self-Dual Codes over Commutative Frobenius Rings [PDF]
, 2009 We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings.
Steven T. Dougherty +7 more
core +1 more source
The [72,36] Type 11 Self Dual Codes from Hadamard Matrices
Davao Research Journal, 2001 Consider a code [n,k,d] of length n, dimension k and of minimum distance d. Let R be a rate defined by the equation R = k/n. Mathematically, the main problem of coding theory is to find codes with large R (for efficiency) and large d (to correct many ...
Rowena Baylon-Cabrizos
doaj +1 more source
Representing Small Identically Self‐Dual Matroids by Self‐Dual Codes [PDF]
SIAM Journal on Discrete Mathematics, 2006 The matroid associated with a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated with a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code.
Carles Padró, Ignacio Gracia
openaire +3 more sources
Construction of new extremal self-dual codes [PDF]
, 2003 In this paper, new binary extremal self-dual codes are presented. A number of new extremal singly-even self-dual codes of lengths 48,64 and 78, and extremal doubly-even self-dual codes of lengths 80 and 88, are constructed.
Harada, Masaaki +2 more
core +1 more source
MDR codes and self-dual codes on Cartesian product codes
Tongxin xuebao, 2010 A Cartesian product code of the linear codes C1 , , C s in 1 , ,Z r Z rs was defined. According to the theorem of submodulo isomorphism, the relationship between the rank of the Cartesian product code C1 × C 2 × × Cs over Z r1 × Z r2 × × Zrsand C1 , C 2,
LIU Xiu-sheng
doaj +2 more sources
Enumeration of Self-Dual Codes of Length 6 over ℤp
Mathematics, 2019 The purpose of this paper is to classify and enumerate self-dual codes of length 6 over finite field Z p .
Whan-Hyuk Choi
doaj +1 more source
Formally self-dual additive codes over F4 [PDF]
, 2010 Additive codes over F4 have been of great interest due to their application to quantum error correction. As another application, we introduce a new class of formally self-dual additive codes over F4, which is a natural analogue of the binary formally ...
Han, Sunghyu +3 more
core +1 more source
Gut microbiome and aging—A dynamic interplay of microbes, metabolites, and the immune system
FEBS Letters, EarlyView.Age‐dependent shifts in microbial communities engender shifts in microbial metabolite profiles. These in turn drive shifts in barrier surface permeability of the gut and brain and induce immune activation. When paired with preexisting age‐related chronic inflammation this increases the risk of neuroinflammation and neurodegenerative diseases.
Aaron Mehl, Eran Blacher
wiley +1 more source
Z₂Z₄-additive formally self-dual codes [PDF]
, 2021 We study odd and even Z₂Z₄ formally self-dual codes. The images of these codes are binary codes whose weight enumerators are that of a formally self-dual code but may not be linear. Three constructions are given for formally self-dual codes and existence
Fernández Córdoba, Cristina +1 more
core