On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

2014 ◽  
Vol 76 (3) ◽  
pp. 373-384
Author(s):  
Masaaki Harada
Keyword(s):  
Dual Code

scholarly journals Nonexistence of Certain Singly Even Self-Dual Codes with Minimal Shadow

10.37236/7155 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Stefka Bouyuklieva ◽  
Masaaki Harada ◽  
Akihiro Munemasa
Keyword(s):  
Minimum Weight ◽  
Dual Code ◽  
Weight Enumerator ◽  
Dual Codes

It is known that there is no extremal singly even self-dual $[n,n/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$. In this paper, we study singly even self-dual codes with minimal shadow having minimum weight $d-2$ for these $(n,d)$. For $n=24m+2$, $24m+4$ and $24m+10$, we show that the weight enumerator of a singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow is uniquely determined and we also show that there is no singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow for $m \ge 155$, $m \ge 156$ and $m \ge 160$, respectively. We demonstrate that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined for parameters $[24m+6,12m+3,4m+2]$ and $[24m+22,12m+11,4m+4]$.

Negacyclic codes of prime power length over the finite non-commutative chain ring 𝔽pm[u,𝜃] 〈u2〉

2021 ◽  
pp. 2150091
Author(s):  
Teeramet Inchaisri ◽  
Jirayu Phuto ◽  
Chakkrid Klin-Eam
Keyword(s):  
Algebraic Structure ◽  
Prime Power ◽  
Nonzero Element ◽  
Dual Code ◽  
Constacyclic Codes ◽  
Chain Ring ◽  
Negacyclic Codes ◽  
Ring Isomorphism ◽  
One To One ◽  
Negacyclic Code

In this paper, we focus on the algebraic structure of left negacyclic codes of length [Formula: see text] over the finite non-commutative chain ring [Formula: see text] where [Formula: see text] is an automorphism on [Formula: see text]. After that, the number of codewords of all left negacyclic codes is obtained. For each left negacyclic code, we also obtain the structure of its right dual code. In the remaining result, the number of distinct left negacyclic codes is given. Finally, a one-to-one correspondence between left negacyclic and left [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text] is constructed via ring isomorphism, which carries over the results regarding left negacyclic codes corresponding to left [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text] where [Formula: see text] is a nonzero element of the field [Formula: see text] such that [Formula: see text].

Concrete and Abstract Information in Semantic and Episodic Memory

1977 ◽  
Vol 41 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Werner Wippich
Keyword(s):  
Episodic Memory ◽  
Semantic Memory ◽  
Memory Retrieval ◽  
Dual Code ◽  
Verbal Code ◽  
Abstract Nouns ◽  
Concrete Words ◽  
Concrete Target

In the present study abstract or concrete target nouns had to be retrieved from semantic memory within 1 min. after the definitions of the nouns had been presented to subjects (Brown and McNeill's paradigm). Following the definition session 22 subjects were unexpectedly asked to recall the target nouns from episodic memory. Semantic memory as well as episodic memory retrieval was better for concrete than for abstract nouns. These results could not be explained in terms of a higher adequacy of definitions for the concrete words. The results seem to support those theories of memory which postulate a dual-code representation of information, especially a verbal code and an imagery code.

scholarly journals On a 5-design related to an extremal doubly even self-dual code of length 72

2004 ◽  
Vol 107 (1) ◽  
pp. 143-146 ◽  
Author(s):  
Masaaki Harada ◽  
Masaaki Kitazume ◽  
Akihiro Munemasa
Keyword(s):  
Dual Code
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