Determining Minimal Degree Polynomials of a Cyclic Code of Length $$2^k$$ over $$\mathbb {Z}_8$$

2018 ◽  
pp. 118-130
Author(s):  
Arpana Garg ◽  
Sucheta Dutt
Keyword(s):  
Cyclic Code ◽  
Minimal Degree

What sort of representation is conscious?

2002 ◽  
Vol 25 (3) ◽  
pp. 336-337 ◽  
Author(s):  
Zoltan Dienes ◽  
Josef Perner
Keyword(s):  
Mental Representations ◽  
Minimal Degree ◽  
Central Claim

We consider Perruchet & Vinter's (P&V's) central claim that all mental representations are conscious. P&V require some way of fixing their meaning of representation to avoid the claim becoming either obviously false or unfalsifiable. We use the framework of Dienes and Perner (1999) to provide a well-specified possible version of the claim, in which all representations of a minimal degree of explicitness are postulated to be conscious.

scholarly journals FINDING THE LIMIT OF INCOMPLETENESS I

2020 ◽  
Vol 26 (3-4) ◽  
pp. 268-286
Author(s):  
YONG CHENG
Keyword(s):  
Model Theory ◽  
Recursion Theory ◽  
Minimal Degree ◽  
Incompleteness Theorem ◽  
Turing Degree ◽  
Turing Reducibility ◽  
Inseparable Pair

AbstractIn this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem ($\textsf {G1}$ for short). We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ (i.e., T is weaker than $\mathbf {R}$ w.r.t. interpretation) and $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds.

scholarly journals On varieties of almost minimal degree I: Secant loci of rational normal scrolls

2010 ◽  
Vol 214 (11) ◽  
pp. 2033-2043 ◽  
Author(s):  
M. Brodmann ◽  
E. Park
Keyword(s):  
Minimal Degree ◽  
Secant Loci

Rational curves of minimal degree and characterizations of projective spaces

2006 ◽  
Vol 335 (4) ◽  
pp. 937-951 ◽  
Author(s):  
Carolina Araujo
Keyword(s):  
Projective Spaces ◽  
Rational Curves ◽  
Minimal Degree

scholarly journals The Binary GOLAY Code Obtained from an Extended Cyclic Code over F8

1980 ◽  
Vol 1 (4) ◽  
pp. 369-370 ◽  
Author(s):  
G. Pasquier
Keyword(s):  
Cyclic Code ◽  
Golay Code ◽  
Binary Golay Code

scholarly journals TRIPLE CANONICAL SURFACES OF MINIMAL DEGREE

2000 ◽  
Vol 11 (04) ◽  
pp. 553-578 ◽  
Author(s):  
MARGARIDA MENDES LOPES ◽  
RITA PARDINI
Keyword(s):  
Minimal Degree

scholarly journals Minimal degree liftings in characteristic 2

2006 ◽  
Vol 207 (3) ◽  
pp. 631-673 ◽  
Author(s):  
Luís R.A. Finotti
Keyword(s):  
Minimal Degree ◽  
Characteristic 2
Sign in / Sign up

Export Citation Format

Share Document