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ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
- Published online by Cambridge University Press:
- 29 April 2018, pp. 159-166
- Print publication:
- August 2018
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- Article
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We study linear complementary dual four circulant codes of length
$4n$ over 
$\mathbb{F}_{q}$ when 
$q$ is an odd prime power. When 
$q^{\unicode[STIX]{x1D6FF}}+1$ is divisible by 
$n$, we obtain an exact count of linear complementary dual four circulant codes of length 
$4n$ over 
$\mathbb{F}_{q}$. For certain values of 
$n$ and 
$q$ and assuming Artin’s conjecture for primitive roots, we show that the relative distance of these codes satisfies a modified Gilbert–Varshamov bound.
ABSOLUTELY ABNORMAL AND CONTINUED FRACTION NORMAL NUMBERS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 16 March 2016, pp. 217-223
- Print publication:
- October 2016
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In this short note, we give a proof, conditional on the generalised Riemann hypothesis, that there exist numbers
$x$ which are normal with respect to the continued fraction expansion but not to any base-
$b$ expansion. This partially answers a question of Bugeaud.
